Eric of Friuli, im Vinzgau

As of 24 Feb 2021, Medlands does not include Eric of Friuli among Gerold and Emma's children. Apart from the posted image in Sources, more than a few scholarly works indicate that Gerold and Eric fought together against the Avars but don't indicate a father-son relationship. They appear after the Wikipedia article.

Wikipedia: Eric of Friuli

Eric (also Heirichus or Ehericus;[1] died 799) was the Duke of Friuli (dux Foroiulensis) from 789 to his death. He was the eldest son of Gerold of Vinzgouw and by the marriage of his sister Hildegard the brother-in-law of Charlemagne.

Most of Eric's tenure was occupied by the job of subduing the Avars. In this he was accompanied by Pepin of Italy and his own father, the margrave of Avaria. In 791, he and Pepin marched a Lombard army into the Drava valley and ravaged Pannonia, while Charlemagne marched along the Danube into Avar territory. Charlemagne left the campaigning to deal with a Saxon revolt in 792. Pepin and Eric continued, however, to assault the Avars' ring-shaped strongholds. The great Ring of the Avars, their capital fortress, was taken twice. The booty was sent to Charlemagne in Aachen and redistributed to all his followers and even to foreign rulers, including King Offa of Mercia.

In 795 or 796, Eric and Pepin, allied with the Western Avar tudun, led an attack which forced the submission of the chief khagan and led to the capture of the Hunorum Hringum, or Ring of the Avars, their chief camp. The khagan was taken to Aachen, where he was baptised as Theodorus. According to the Annales Fuldenses, the khagan was killed by his own men.

According to the Annales Laurissenses, Eric sent raiders against Pannonia in 796 under Vojnomir, duke of the Pannonian Croats.

Some time between 787 and 796, Paulinus of Aquileia wrote a Liber Exhortationis for Eric. The work draws from the Bible and certain Fathers of the Church to offer instruction on how to live a morally upright Christian life while carrying out secular duties.

In 799, Eric was killed at Trsat (Tharsatica) in Liburnia by the treachery of the inhabitants according to Einhard. His father died on the eve of battle with the Avars that same year.

Notes: 1. It has been suggested that his name is a mistranscription of Munichis.

Sources
Einhard. Vita Caroli Magni. translated by Samuel Epes Turner. New York: Harper & Brothers, 1880.
Wallach, Luitpold. "Alcuin on Virtues and Vices: A Manual for a Carolingian Soldier." Harvard Theological Review, Vol. 48, No. 3. (Jul., 1955), pp. 175-195.
Ross, James Bruce. "Two Neglected Paladins of Charlemagne: Erich of Friuli and Gerold of Bavaria." Speculum, Vol. 20, No. 2. (Apr., 1945), pp 212–235.
Hodgkin, Thomas. Italy and her Invaders. Clarendon Press: 1895.

Regarding the death of Duke Eric - from an academic paper published by Nenad Labus "Tko je ubio vojvodu Erika?" (Who killed Duke Eric?) 2000 "the Frankish sources actually state: Eric's death is to be connected with the death of the Bavaraian prefect Gerold and both of them were victims of Avarian hands because they had entered a war which the Avars wanted to prevent."

Book and Passages Not Confirming Parentage

Roland Greene, S. C. (ed.) (2016) in The Princeton Handbook of World Poetries. Princeton, NJ, USA: Princeton University Press, p. 362. Snippet Available at: Google Books.

Dales, R. C. (2022) “The First Generation of Carolingian Scholars,” in The Intellectual Life of Western Europe in the Middle Ages. Leiden, Netherlands: E. J. Brill, pp. 85–86. Available at: Google Books. Note: Paulinus does not mention a father-son relationship.
"[Paulinus] was a poet of considerable originality, skill, and deep feeling. When in 799 Duke Eric of Fruili fell in battle against the Avars, Paulinus composed a beautiful rhythmic dirge lamenting the death of his friend and lay adjutant, ending with the plea:
"'Eternal God, who from the dust formed in your image our first parents through whom we all perish, but who sent your own beloved son through whom we all miraculously live, redeemed by his crimson blood and holy flesh, grant to your sweet servant Eric, I bet you, the joys of paradise both now and through the unmeasured aged to come.'"
Source: Pohl, W. (2018) “The Century of the Griffin: The Collapse of Avar Power,” in The Avars: A Steppe Empire in Central Europe, 567–822. Ithaca, NY, USA: Cornell University Press. Available at: Google Books. ISBN: 9781501729416. Note: This eBook source is scholarly and highly rated. Owning a copy is the recommended.

"More attention is devoted in the annals to the war against the Saxons or the conflicts in Spain than to conditions in the land of the Avars. In 797 a Lombard-Bavarian army under Eric of Friuli was probably once again active in Pannonia; the Alemannic annals also mention King Pippin’s struggles with Slavs.[367] At the end of the same year an Avar embassy with rich gifts attended Charles at Herstelle.[368] Unfortunately we do not know which of the Avar princes had sent it. In 798, Arn, bishop of Salzburg, was promoted to archbishop, not least in the context of the Avar mission. In January 799, Alcuin inquired of him by letter “what Avaria does and believes.”[369] Yet progress was clearly slight. When rebellion broke out in the east in 799, Alcuin observed critically: “The loss of the Huns, as you say, is due to our negligence.”[370]

"Frankish policies in the southeast did, in fact, suffer a serious reverse in 799. As the Avars revolted, the two responsible commanders of Carolingian forces, Duke Eric of Friuli and Gerold, prefect of the eastern territories, were both killed in the same year, though neither died in battle with the Avars.[371] Eric “fell victim to an attack by the residents of the city of Tarsatica in Liburnia.”[372] Tarsatica/Trsat, on a hilltop in present-day Rijeka, belonged to the coastal strip of Liburnia that had remained under Byzantine rule in the seventh century. Apparently, the Franks now claimed sovereignty over the city, as they did over the Istrian Peninsula. That the populations of these old Roman cities were dissatisfied with the Frankish functionaries is demonstrated by the grievances voiced in the so-called Placitum of Risano held a few years later near Koper in Istria.[373] The attack on Eric by the townsfolk of Tarsatica suggests that they had Byzantine backing.[374[ The Byzantines may also have encouraged the revolt of Avar groups. Paulinus, patriarch of Aquileia and a skilled poet, honored the fallen Eric with a poem that reveals the tension between dreams and realities of Frankish expansion.[375] Among the cities that grieve for him, first named is Sirmium, desolate but still linked to imperial traditions; then follow the urban centers of Istria and Friuli. The poem then culminates in a vision in which Scythia, the marshes of the Sea of Azov, and the Caspian Gates appear as potential targets for imperial expansion. The victory over the “Scythians” of the Carpathian Basin extended the Carolingian horizon to include the vast spaces of the ancient geographers.

"However, the death of the Carolingian commander Gerold, on September 1, 799, also fell short of these new vistas opened up by the Avar war. Einhard recounts that Charlemagne’s brother-in-law was killed with two companions, “uncertain by whom,” while inspecting the troops before the battle against the Avars.[376] The Royal Frankish Annals are silent about this murder mystery and have him die an honorable death in battle.[377] The double loss of Eric and Gerold deprived the Franks’ Avar policy of its principal leaders, and it is unclear whether the revolt was put down that year.[378] A few years later, in 802, unrest in Pannonia again claimed the lives of two high-ranking individuals. The counts Chadaloh and Goteram died during an Avar attack at “castellum Guntionis,” together with many others.[379]"

Source: Airlie, S. (2005) “The Aristocracy: Captains and Kings,” in Story, J. (ed.) Charlemagne: Empire and Society. New York: Manchester University Press, pp. 94–95. Available at: Google Books.

“Those who governed in the name of Charlemagne were also warriors. Gerold fell in battle on the frontiers of the empire in 799, as did Eric, duke of Friuli. Both men were commemorated in poetic epitaphs that attest to their status in contemporary eyes as Christian warriors and governors.[21] But it was also remembered that they had fallen in Carolingian service. Einhard takes the details from the Royal Frankish Annals on the death of Eric and Gerold, and artfully places both deaths in a section dealing with Charlemagne ’s successful management of the war against the Avars. Towards the end of the ninth century, Notker, writing in the monastery of St. Gallen where Gerold was remembered, drew on the memory of his campaigns in order to write his account of Charlemagne’s wars.[22] Thus the military activities of these men were subsumed into representations of Carolingian rule. This also reflected the historical situation. Eric assuredly profited from the campaigns against the Avars, but it was to Charlemagne in Aachen that he sent the captured treasure.[23]

“That men such as Eric and Gerold were Christian warriors cannot be doubted. As we have seen, contemporaries represented them as such and the importance of this aspect of aristocratic identity should not be underestimated. In the late Carolingian period there is an example of one aristocrat, Gerald of Aurillac, who found that his Christian identity clashed directly with his secular aristocratic code, and it was the latter that had to yield. Gerald may have been an extreme case, and that his Life presents him as a bit of a misfit may tell us more about Gerald’s clerical biographer than about the historical Gerald. Nonetheless, Gerald’s Christian conscience could have been real enough and the clerical authors who represented clashes between Christian values and the secular ethos of aristocratic warriors were themselves from the ranks of that aristocracy and knew that dilemma at first hand.[24]”

Notes
21. Epitaph of Count Gerold, MGH, PLAC I, p. 114; Verses on Duke Eric, MGH PLAC I., pp. 131-3. See also Ross (1945)
22. RFA 799; trans. King (1987), p. 130; Einhard, VK, c. 13, trans. Dutton (1998), p. 24; Notker, Gesta Karoli, II, preface, MGH SSRG NS XII, p. 48, trans. Thorpe (1969), p. 134.
23. RFA 796; trans. King (1987), p. 89.
24. Airlie (1992).

Source: Hodgkin, T. (1899) “Pope and Emperor,” in Italy and Her Invaders 774-814: Book 9: The Frankish Empire. Oxford, UK: The Clarendon Press, pp. 182–183. Available at: Google Books.

"The autumn of this year (799) was saddened for Charles by the tidings of the death of two of his bravest warriors, slain in battle with the barbarians of the Danube. Gerold, duke of Bavaria, brother of the beloved Hildegard, was slain with two of his officers by a troop of insurgent Avars, while he was riding in front of his followers and cheering them on to the encounter; Eric, duke of Friuli[1], fell at Tersatto[2], the victim of an ambush laid by the barbarous Croatians. The scene of this disaster, together with other indications[3], shows that Istria now formed part of the Frankish dominions: an important conquest, to which we are unable to assign a date, save that it must have been before the year 791. The death of Eric was an especially heavy blow for his royal master. It was he who had penetrated (795) into the far-famed and mysterious Avar Hring, and carried off its stored- up treasures. He had been a generous benefactor to the Church, a liberal almoner to the poor, and in all things, as far as we can trace his actions, a type of the Christian hero. His friendship for Paulinus, bishop of Aquileia, who composed for him a manual of the Christian life called ‘Liber Exhortationis,’ and who lamented him after his death in a dirge which recalls David’s lament over Jonathan…”

Notes
1. Eric had been preceded by Marcarius (Cod. Car. 65), who may probably have replaced Hrodgaud.
2. Near Fiume in Croatia.
3. Chiefly the fact that in a letter written in 791 (Ep. Carolinæ, 6, ed. Jaffé), Charles speaks of the ‘dux Histriæ’ as his vassal.