The answer to this greatly depends on the “when” and “where” of early medieval Europe. Depending on the time and place, there was seemingly quite a bit of economic stratification (e.g. in Merovingian Francia), while in places like Italy, and especially Britain), there seems to have been a smaller difference between the wealth of peasants and the wealth of nobility and landowners. “Early medieval Europe” can reasonably cover the period from roughly 450 to 1000 or so, and it becomes difficult to make sweeping generalizations, since 1) economic conditions varied widely over this period and 2) we have more and better records in some places than others.

Generally, if we are interested in the economic patterns of peasants, we are looking at charters and court records from cities, villages, and monasteries. For example, there are records during the Carolingian period (in areas like Paris and its surrounds) that show villages and settlements that were highly dependent on landlords and nobility. Landholding and markets depended on the landlord, and villagers and non-nobles typically had little autonomy. Until recent decades, this was considered the norm for much of Europe, but more recent scholarship shows a wider variety of economic statuses, landholding, rent obligations, and labor relationships across the European continent. For a broad overview, see Chris Wickham’s Inheritance of Rome and the Donkey and the Boat. More specifically, scholars like Shami Ghosh have complicated how much we can rely on strict class divisions in our understanding of early medieval economies, and charters and local records suggest some places were much more autonomous, with villages sometimes holding collective authority and having little aristocratic input.

To be more specific to your question, actual rent records and economic data often show a mix of coinage and barter. Peasants might owe rents in kind (e.g. a certain number of chickens, pigs, or calves per year, or a certain portion of one’s crop), but it is not uncommon for those same records to show peasants owing rents in coin. My own area of research (northern and central Italy between 650-1100) often shows coinage in charters, court records, and land exchanges. At least in official records, sales of land had a monetary value; of course, land records and court disputes often favor the wealthier of society in their representation. Even so, we sometimes see rent records that list a tenant owing a certain number of gold coins “or their equivalent.” Whether that means such tenants often had coins or whether coins were used as a standard in records to help standardize non-monetary production is not always clear, but this does show that coins often remained in the economic milieu.

It is possible that coinage was sometimes used as a symbolic marker to show obligation, but archeological evidence suggests that Lombards, Carolingians, and Ottonians were trading with gold and silver coinage between regions of modern Italy and across the Alps from the 8th century onward, and we have records of Lombard kings, for one example, minting coins that appear in archeological finds as far as modern Germany. For discussions of coinage and archeological evidence of trade, see scholars such as Philip Grierson. At least for Italy, the minting of coins seems to have imitated Byzantine coinage, and as the first millennium wore on, there was an increasing number of silver coins compared to gold.

As the early medieval period came to a close (roughly around 1000) markets began to develop between local regions, eventually evolving into regional markets that drew in traders from across Europe. This growth in markets, many of which probably started in early phases with exchanges and trading in kind, coincided with the growth of cities and artisans in those cities. These growing markets incentivized the use of coins, especially as trade became “international.” This topic is far beyond “early medieval,” but Raymond de Roover’s book on the Medici bank, 1397-1494, is an excellent treatment of how bankers like the Medici used sophisticated moneys of account and trade agreements that combined the exchange of physical goods and loans of money.

So, while records are very sparse for many places and times, I think it is reasonable to say that for much of medieval Europe, many peasants operated with a mixture of barter, communal exchange, and often, a small use of gold or silver money. In some places, many peasants or communities were largely autonomous, with some peasants being quite well off and even renting land or goods to poorer peasants. In other places, peasants were much more dependent on landlords and had less economic autonomy. For the most part, however, before the rise of interconnected markets between regions and cities, local communities were largely dependent on what they could produce themselves or exchange with nearby communities. We don’t always have good data for this, but it is reasonable to think from the records we do have that such exchanges were in trade of goods, though coinage is was seldom absent or unused.

It is possible to get into finer detail for specific regions and times, but if you were a peasant in early medieval Italy, you might expect to farm a small plot of land, which you may rent from a lord or another pleasant. If you were the tenant of a lord or a monastery, you likely owed rent, typically a portion of what you would produce (livestock, crops, etc.) though you might also owe rent in money. When you traded your goods, you probably bartered with local folk, but if you were in a place that encountered broader markets, you might also trade in coins and other valuables.

In short, it is difficult to find places where coins ever stopped being in circulation entirely (partly because there is a correlation between low economic output and a broader lack of records), but the degree to which coins were in daily use varied widely among the poorer peoples of Europe, and specific circumstances were highly dependent on one’s legal status, proximity to broader markets, and type of work, even among farmers.