It depends. Manorial methods and customs varied a great deal from region to region and even manor to manor, and they also varied across time, especially from the 14th century on. Your social status as free peasant or serf might also affect a change of lords. (Around half of English peasants were serfs until the 1400s, though by the 1300s there wasn’t a whole lot a distinction between serf and free; how much land you possessed was the main distinction. There was also a distinction between personal servility and holding land by villein tenure.) There was a good chance you would never have met your lord. He (or she) might reside far away on another manor; your manor would be under the supervision of one of his estate agents (in some cases called a “reeve”).

All this aside, the main thing maintaining peasant stability in the face of change was the custom of the manor, which peasants jealously guarded. If their lord or his supervisor tried to introduce new customs—like new labor obligations or new fees—peasants would complain about and resist these innovations in their regular manorial courts (which were more about the day-to-day administration of the manor and its tenants than about weighty legal issues). If you lived on a manor that was part of the “ancient desmesne”—manors once held directly by William the Conqueror—you were a “privileged villein of the ancient desmesne” and thereby free of certain tolls and obligations and enjoyed legal privileges not available to other peasants. You might even live on a manor where you and your fellow peasants has bought your freedom from meddling in the life of the manor by agreeing to pay him an annual collective fee.

If your lord was a member of the gentry (say an ordinary knight with just one manor) and lived on your manor, when he died you would be expected to renew your personal oath to his heir or whoever next received the manor. Likewise, if you died, your heirs would be expected to pledge their loyalty to the lord. But the custom of manor would prevent dramatic swings in how a change of lords affected your life. As personal servility and villain tenure began to collapse in the face of the peasant labor shortage caused by the Black Death (arriving in England in 1348), peasants got a lot more freedom and control over their lives. In the face of a labor shortage caused by the mortality, they could sell their labor to the highest bidder. The Statute of Labourers of 1351 was an unsuccessful attempt to reign in rising peasant wages and the movement of peasants from one manor to a higher paying other. The old school analysis argued that when lords tried to re-impose elements of serfdom to keep peasants working on their land, this helped spark the Peasants’ Revolt of 1380. In other words, an attempt to dramatically shift peasant custom led to social unrest. More recently, Mark Bailey (The Decline of Serfdom in Late Medieval England: From Bondage to Freedom) has argued that there is little evidence that lords in large numbers were doing this. In any case, by the time of the War of the Roses, serfdom had almost died out; peasants held land through leasehold. As long as you paid your annual rent to the lord, a change of owners would have minimal effect on you.

Sorry, I can’t answer for land conditions in early medieval France (BTW, it was still called “Gaul” in official records, for instance church stuff, throughout the MA.) I seem to recall that some French peasants were expected to renew their oaths to their lords annually.

can i tack on a request for late antique (or early early middle ages) gaul? been reading some of the primary sources and it seems interesting

Can I add a precision request?

Was the feudal system codified in any way so that it was pretty much the same everywhere, or were there significant variations between region to region or "country" to "country"

I am not talking about changed like size of lots, but on the responsabilies and right?

Everyone seems to talk about the feudal system in the middle-ages as if there was only one, implying the rights were the same everywhere for peasant farmers and for lords.

Was it really the case?