The concept of freehold tenure is pretty central to the book. Not sure you could get any more on-point for the general reader looking for a book recommendation.

But since you ask: the peasant's rights to land were exquisitely bespoke. No tax collector could figure out how much one family owed versus another in another county. The rules in one prefecture of one county may have been completely unresolvable with the rules of a county a hundred miles north. Everything was negotiated family to family over generations, with rights in one place having no corollary whatsoever with the rights in another area, making the tax man's duty a fool's errand.

So, I don't your first statement "European peasants "renting" the land they farmed had much stronger ownership rights than Americans who "own" land do today." is really meaningful. Because no generalization can be made about the rights of a European peasant. That problem is the whole reason for the systems of freehold tenure that prevail today: making the territory "seeable" by the state.