This is a big question and I will only attempt to answer this in the broadest sense, but do let me know if you have any further questions.

Firstly, it is important to note that the interconnected trade networks binding the Mediterranean world together was already breaking down, especially as the Roman state declined in the west. Without the state as a massive consumer driving up demand and fueling other parts of the economy, only wealthy aristocrats in important coastal cities, such as Rome and Marseilles, were able to still import expensive goods from abroad, an important indicator of long-distance trade, such as the high quality pottery from North Africa. The idea that this network broke down in the seventh century due to the Arab conquests was the brainchild of Henri Pirenne, but his thesis was from the early twentieth century and an argument most succinctly summed up in his Muhammad and Charlemagne (1937). Suffice it to say, scholarship has long moved away from this position. For one thing, Pirenne relied largely on the literary sources and scoured them for indicators of international trade, primarily luxury goods - unfortunately luxury goods are not great at telling us about ordinary trade. With the huge advances in archaeology that we now possess, we can determine that trade as a whole was declining, so identifying the principal cause as from the seventh century is incorrect.

The picture can further be nuanced when we consider that it was in the sixth and seventh centuries that Merovingian Gaul experienced economic growth not in the south, but in the north, where a new North Sea-centred economic zone began to coalesce. New emporia were created throughout this region, such as Hamwic (future Southampton), and it was due to this trade that during the Carolingian period, in the eighth and ninth centuries, that new elites were able to become wealthier than before - events in the Mediterranean were secondary to this growth, since the economy, due to the breakdown of the centralised Roman state, had been becoming increasingly regionalised for centuries by this point. In Chris Wickham's study of the early medieval economy, he pointed out that after Egypt, which was famously fertile, Frankish aristocrats were the wealthiest amongst their contemporaries. Did they bewail the fact that they now lived in a new 'Dark Age'? Hardly. As Peter Sarris put it, whilst the Roman empire was facing repeated crises in the seventh century, the west was becoming more assertive and its political elite more coherent. A new, admittedly more regional, order was already being created and we need to acknowledge the vibrancy within the developing Frankish and Anglo-Saxon kingdoms, not their supposed decline.

It is therefore a mistake to 'blame' this economic downturn on the Arabs. Piracy was certainly a factor, but it is unclear how much of an effect it had on trade as a whole. For one thing, how on earth can we find evidence for this decline? It is in the late seventh and early eighth centuries that we have two particularly vivid examples of northwestern Europeans going to visit the Holy Land, the Frankish Arculf and the Anglo-Saxon Willibald. They had not been deterred by Arab raiders, but instead seemingly visited Arab lands that were accustomed to western visitors wishing to visit important Christian sites. War is indeed bad for trade, but that's hardly limited to the Arabs - we can for example look at Emperor Justinian's Gothic War in the mid-sixth century, which is generally seen as being ruinous to the previously relatively stable Italian economy and aristocracy. From another perspective, we can also see the burgeoning slave trade from western Europe to the caliphate as a cause of economic growth (though morally speaking this is obviously heinous), since people is the one resource that the west had in abundance and which could be exported in return for the fabulous wealth of the east, explaining in part the continuous attestation of eastern objects in the west - though some trade declined, other forms of communication not identified by Pirenne remained intact, and it is simply incorrect to say that Christians were now closed off from the Mediterranean.

It is far too simplistic to attribute something as broad as the 'Dark Ages' (which wasn't even a thing, and the 'early middle ages' is the preferred term amongst historians) to a single cause. This instead reminds me of the many polemicists today who seek to foment Islamophobia, who find in the Pirenne thesis an argument that they could reshape to suit their own distasteful ideological ends. Modern scholarship however presents a very different view, and we should instead look to the weighty tomes of Chris Wickham and Michael McCormick, Framing the Early Middle Ages: Europe and the Mediterranean, 400–800 (2005) and Origins of the European Economy. Communications and Commerce, A.D. 300-900 (2001) respectively, to explain the complex, and far from always declining, European economy of the early middle ages.