In Mohammed and Charlemagne (1937), Belgian historian Henri Pirenne argues that Antiquity lasted longer than previously thought, notably because the roman trade network throughout the Mediterranean continued long after the fall of the Western Empire and was used by the Germanic kingdoms, and really ended with the Arabian conquests and dominance in trade and piracy from the 7th Century onward. Is this thesis commonly accepted today? I know labels are not perfect and naturally it was more of a transition than a fracture, but did Antiquity actually ended in the early 7th Century, rather than the traditionnal 476 date?
Not really, no. Pirenne was undoubtedly a great early pioneer in medieval economic history, but the passage of time has not been kind to his thesis. Archaeological evidence contradicts a lot of his statements about trade. For example, the Oxford archaeologist Bryan Ward Perkins has argued in his brilliant yet controversial book "The Fall of Rome and the End of Civilisation" (2002) that the Mediterranean trade network, manifested in things like North African red slipware turning up everywhere from Italy to Wales and from Portugal to Hungary really broke down between 400 and 550 as a result of the collapse of the Western Roman Empire and Justinian's even more destructive attempts at reviving it. Meanwhile, Adriaan Verhulst in "The Carolingian Economy" (2003) has argued that the 8th century didn't see the Western economy descend into rural autarky and that the period 750 - 900 was an age in which long distance trade continued, such as in the North Sea, and burgeoning rural markets for peasant producers developed. Some historians remain broadly sympathetic to Pirenne's idea of the ancient world lasting beyond 476 i.e. Peter Brown's "The World of Late Antiquity, 150 - 750" (1971, reprinted 2013) is a massive nod to Pirenne, and Guy Bois takes it even further in his "The Transformation of the Year 1000: the village of Lournand for Antiquity to Feudalism" (1992) in which he argues that the real end of the ancient world happened at the end of the 10th century with the end of ancient slavery and of the ancient state (the Carolingians essentially being its life-support) and the birth of classic feudal society. But yeah, most historians consider Pirenne to be incredibly outdated and also somewhat politically incorrect too, regarding his portrayal of Islam to be too monolithic and orientalist (in Edward Said's sense).
/u/chevalier-sans-peur points to some excellent sources. In my own work, I tend more toward the surveys by McCormick and Wickham. These are both heavy tomes and are probably best treated as encyclopedias with decent introductions than cover-to-cover reads, although McCormick has also published a shorter summary. Both think a lot about archaeological evidence, much of which hadn't yet been excavated when Pirenne wrote. An important early survey of this evidence was by Hodges and Whitehouse back in 1983, although an even earlier response by Sture Bolin (first published in Swedish in 1939) had already pointed out that Scandinavian hordes had a lot of potential to yield information about early medieval trading connections. For a good look at the influence of Pirenne's thesis, as well as the perhaps more pressing problems that it can distract us some, see the recent article by Bonnie Effros. I'd also follow /u/chevalier-sans-peur with the recommendation of Peter Brown, who despite nodding at Pirenne actually examines cultural continuities and eventual change of Late Antiquity rather than the economic discontinuities that preoccupied Pirenne. It's a completely different look at the period, and it might be complemented by Julia Smith's more recent survey.
Basically, Pirenne argued that the Islamic conquests broke the old Mediterranean trade networks apart, but scholars now agree that Mediterranean trade had collapsed before the Islamic conquests. In the west, this probably happened in the 400s, and although there were important cultural continuities in North Africa, Iberia, and Gaul, things were pretty grim north of the Loire and into Anglo-Saxon England. The Eastern Mediterranean chugged along much later, into the 600s, but then it too collapsed on the eve of the Islamic conquests. There were a lot of factors at stake, including plague and war. Wickham emphasizes that in most places, diverging local and regional developments were probably more important than these transregional stories, while McCormick's interest actually lies with the development of new routes for connections and commerce beginning in the late 700s. Overall, it seems that the Islamic caliphate had the opportunity to grow because of the preceding collapse. It was in turn a stimulus that generated new economic growth, both by reconnecting regions that had been growing apart and by establishing a new cultural elite who generated increased demand for interregional trade goods (both luxury items and slaves).