My error was to confuse centralization with unification. So, my real question was :
Can the King of France unify his kingdom without hugely expand the Royal Demesne ?
Not without having a clearly dominant position. Early Capetians kings, while having a direct power on Ile-De-France (that was quite a wealthy region) and beneficing from an important institutional power, needed to rival with their most powerful neighbours to be able to deal with them.
Expansion of royal demesne wasn't a matter of choice when it come to unification of the realm : a feeble prince couldn't have done that.
And once you put yourself stuck in the process, it's hard to get rid of it because it would mean concede parts of your hegemony.
Conquest, inheritence or confisque (confiscation of a fiefdom when the vassal was considered no longer fulfilling his obligations) followed pretty much quickly as more the kings authority grew, more resistance you had against this process.
Apanages, first concieved as giving part of the demesne to sons that didn't inherited the crown, were used in order to create "feudal protectorates" (in lack of a better word). They could be quite important and cover 1/3 of the realm, and eventually managed to "prepare" the reunion to royal demesne by applying similar inner policies than royal ones (not that they were forced to, but simply because they were the ones they were used to) : administrative, economics, military, etc.
Not counting they could be gained more easily trough inheritence (not only because of familial ties, but because an Apanage was supposed, when the main line died out, come back to royal demesne even if there were more direct heirs).
At some point, after the HYW, while great feudal demesnes still existed in France, you had a too important royal demesne to be ignored. At this point, either feudal lords complied (as the County/Duchy of Nevers that was never part of the royal demesne up to 1789, but trough several edicts was treated as an apanage, then as a protectorate de jure), or if they didn't (or if they were suspected to pose a threat)
they were removed.
You can't really have both a Capetian/Valois king unifying the realm (implying a strong royal demesne would it be only to have the ressources to impose his full authority) and surviving (at a worth of mention scale) classical feudality.
But could this definition be alternated in an ATL? For example under the influence of the Roman Law?
At the moment Roman Law (as in Justinian corpus, as Roman customs were maintained) was reintroduced in the XIIth century, feudality as an institution was very well established.
Furthermore, feudality definition is an historiographical one : critically in an oral society based at least as much on custom than law, making feudality a really proteiform concept when it comes to definition.
Because of that, the definition is forced to be vague and reduced to the lowest common denominator, and hard to be changed even if atypic forms of feudalism appears (as Occitan, Catalan or Hispanic feudalism; based more on written agreements, less on customs, with a more important presence of late Roman law, etc.)
But, I believe that it could be done (for example by Philippe II or Louis IX).
You make a mistake by separating Plantagenet situation from "feudalistic minds". What Henri II based his power on was feudalism, in a specific variant, that didn't went against this system was.
You really, REALLY, need to understand that institutional and political differences there didn't came out of nowhere because "they changed their minds" but because of the different conditions.
Again, compared to practically every continental realm (except maybe Scandinavia), England was underpopulated, and also had a really reduced nobility (essentially because Normans get almost entierly rid of Saxon elites).
Philipp II ruled over a quite different kingdom : more populated, with a more important nobility and where free-men didn't made less than 1/3 of the kingdom (that I remind you, was at best inhabited by 1,5 millions of people) and where nobility didn't had three centuries to fully establish themselves as independent powers.
And for Louis IX. Why should he bother to compromise with great nobles when he could say "Do as I told, or else".
Else being pushed into the great nothingness with the help of a modern army, huges ressources from an already huge demesne, and from the benevolent help from possible heirs.
You could ask Armagnacs about that, if Jean V didn't died from a sudden and unexpected double attack of poignarditose and of Syndrome of-Axe-In-The-Head (named after the doctor Axe-In-The-Head) in the middle of a siege; or if his wife wasn't forced to abort.
What I had detested in the french history is to seeing the dukes and counts playing they politics like they were truly independents. Territories conquered by the kings and give away to they children (the apanages) and those one feeling very litle loyalty to the crown (barely to the king that happens to be they father or brother).
1) And why exactly should they not do that, regarding a territory that was legally and mentally their own property?
2) I can give several exemples of the contrary : Alphonse de Poitiers, Second Angevine House, most of Bourbon House up to the XVIth century, Philippe d'Orléans, etc.
Not considering the fact some royal heirs were trusted with their own apanages, you really underestimate the ideological and political strength of dynastic ties in a political organisation that is basically based on these.
I'm a little frustrated about that it seems that the way how France become France is peaty much deterministic. It should happens in the OTL way or it will disintegrates itself, or conquered, or splited, or something like that. What I search is for a different patent but not one so radical that France will not be France...
Well, that's pretty much that : France, historically, had very strong tendencies to division. Because of its huge population (remember that it had the most important population in Europe up to the XIXth century) that implied a more fragmented administrative and political managment (You don't rule over 8 to 20 millions of people as you rule over 1 to 3); political geography (Gallo-Roman pagi's boundaries being more or less the direct ancestor of feudal entities, a pagus more or less including a same folk within his borders); linguistic differences; etc.
After some reflexion, you'll agree that either the whole thing go even more divided, or that the necessity of unifying all of this entierly should strikes someone. Especially if "someone" have already an institutional suzerainty over all the place and a good pretext to evict rivals.
Giving the initial historical conditions of how France appeared, that pretty much limit the choices.