The Imperial French/Burgundian/
whatever you may wanna call it culture would be one of the rather obvious results of a redefinition of culture, and it would be one that I would be pleased to see, yes

The difficult question here is how far we have the culture extend, and that depends on the exact general model of culture that we employ. We have two possibilities:
a) a strict legitimacy model, i.e. a separate culture is only given to separate political and legal entities (EDIT: or perhaps better, as Norrefeldt put it, areas with a separate political and legal culture). Under this model, the culture would only be justifiable as "Burgundian" culture for the Kingdom of Burgundy, which covers the EU2 provinces of Provence, Dauphiné, Savoie and Franche Comté. Lorraine and Luxembourg would have to be German then.
b) a combined model taking into account both legitimacy and language/ethnicity/"nationality" and distributing culture on a less general and more case-to-case base, depending on which of these factors was more important (in the sense of resulting in the ingame effects of culture) in a given area and on which setup is most desirable for game balance and the game flow. Here, we could construe an "Imperial French" culture for the provinces that had a majority of French-speakers, but were part of the HRE and used to imperial law
I'm inclined to prefer the second model actually, simply because I think it would be unwise to implement "ugly" cultural setups just for the sake of sticking to a fixed principle. The advantage of the "Imperial French" solution is that it would allow to make Luxembourg a state culture province for Burgundy and Spain as well, which will strengthen Burgundy and make the province worth keeping and fighting for for Spain.
The drawback of a combined model is of course a loss of clearness and consistency.