This is an awesome question, and a depressingly under-studied one. Much of the historiography in this subject is 30+ years old, so you'll have to keep that in mind (although my PhD deals with some of these same issues, so check in with me again in 3-4 years to see if I've discovered any new insights!). Finally, before we start, a hat-tip to /u/LukeInTheSkyWith and his overlooked posts rundown in the Sunday Digest, without whom I never would have even known this thread existed!

So I'm actually going to chicken out a little at the start and tell you about where free peasants fitted into European society in 9th-10th century Europe first. Things varied hugely on a regional basis, with some areas being dominated by large landowners (the church and the greater aristocracy), such as the Paris basin, where free peasants and smaller landowners were pretty rare; other areas were made up almost entirely of smallholders, with very few large landowners, such as Brittany or many Alpine valleys. Finally, there are those areas in-between, like Burgundy or Swabia, where there was a mix of large and small landowners, including multiple owners of a village. Peasant landholders had varying degrees of autonomy depending on the situation - in a landscape like Paris they had much less than in Brittany, for example. In a mixed environment, peasants seem to do a lot of playing larger landholders off against one another in order to maintain autonomy in the village and to avoid a monopoly on power by one player. For example, when new monasteries are founded, they often have a large amount of local support in order to provide an alternate locus of wealth and patronage, until they become too powerful and a threat themselves to the local independent peasantry.

I've started off with the earlier period because this is much better understood than the post-millennial period, with a lot of nice detailed studies based on monastic records. The best place to start is probably Chris Wickham's The Inheritance of Rome, chaps. 9 & 22, which provides a nice, easy introduction from which I've cribbed a lot of the paragraph above. It's also chock-full of further reading.

The problem with the 11th and 12th century is that developments get muddied by becoming enmeshed in the debate on the seigneurie banale and the 'Feudal Revolution'. As I'm sure you know, the classic model is that of Georges Duby: as small, castle-based lordships were established across Europe at the beginning of the 11th century, the distinctions between free and unfree peasants which had previously been important in determining the status of the peasantry was undermined, becoming less and less important as the new 'banal lords' enforced exploitative customs and dues on the entire peasantry within their lordship, regardless of legal or tenurial status. This paradigm was developed by Duby's successors, notably Pierre Bonnassie, who saw the early middle ages as a 'golden age' of the free peasantry between the slavery of antiquity and the imposition of 'serfdom' by the banal lords of the 11th century. This work culminated in syntheses on medieval society as a whole by Robert Fossier (Enfance de l'Europe) and Jean-Pierre Poly and Eric Bournazel (La Mutation Féodale) in the 1980s. But, of course, the 1990s saw a big fightback against the whole paradigm of medieval development laid out by Duby and his followers, led by Dominique Barthélemy and Stephen D. White, which left big holes in our understanding of the place of the peasantry in 11th-12th century society. Sadly, nobody has really produced any work which has attempted to plug those holds. The closest anyone has come (to my knowledge anyway) is Laurent Feller's economic history survey Paysans et seigneurs au Moyen Age, which deals with the issues in chap. 3 (and a bit in chap. 4). However, he ducks the issue more than grappling with it head on, and focuses almost exclusively on Italy for evidence of the 11th century. This is understandable, as he's an Italianist, but problematic because the legal culture and economy in Italy is significantly different from the rest of Europe in this period, due to the importance of cities and the longer survival of public courts and lay legal notaries.

So, what's the deal with free, autonomous peasant landowners in the 11th and 12th centuries? We really don't know. They certainly recede from view in the documentary sources, and are almost invisible by 1100. So something's happening. But how exactly that disappearance is to be interpreted is a very different matter, and one which is still open for debate.