I think the problem is that the EU used to be just an extension of French foreign policy, with a docile Germany and an occasionally recalcitrant Britain which nevertheless actually implemented the EU regulations it agreed to whereas in France, actual implementation was, shall we say, more selective.
Foreign policy has remained outside the remit of the EU and the EU has mainly let France do what it wants in Africa. With regard to most other areas NATO has dominated the agenda and France had put itself a bit out of play by exiting the command structure under De Gaulle (it will re-enter in April).
As for implementation, French implementation is mainly slower than British implementation. Where French compliance has been a problem this has mainly been due to corruption rather than calculation by the political leadership.
That's an unnuanced view.
I am being polemical because I find it ironic that an appartent CP supporter should appear to endorse imperialistic notions of French Grandeur and Noblesse Oblige in France's relations with its smaller neighbours. This harks back to an earlier conversation where quite racist, supremacist, and imperialist attitudes were expressed towards Ireland and all things Irish. (The type of attitudes, which if promulgated more prominently as representative wider "European" attitudes, would guarantee a much higher No vote the next time around).
I would have hoped that the French Left would be more internationalist, multi-lateral and respectful in its tone to fellow members - building alliances rather than whipping up nationalist antagonisms. France does not have a monopoly on progressive tendencies in Europe and portraying other polities as overwhelmingly composed of dimwitted peasant dupes of Global capital is not generally a good strategy for building a united progressive movement throughout Europe. notes from no w here