I have done some reading on this here and elsewhere. It's my belief that the better the child's memory, the more likely they are to prefer to rely on it rather than learn phonics. In a child with a fantastic memory and strong will (read as "bull-headedness") this can cause a lot of resistance to learning phonics.
So I'd say your kid sounds normal for his type. It's how I learned to read early and well, so it's hard to say that he is doing it "wrong", although I see a lot of value in phonics rules and taught them to my son at every chance. Today he is able to read and spell a large variety of words because he learned the phonics rules. Was it necessary, though? Probably not. A smart kid who has memorized a huge number of words is bound to notice enough rules to be competent at assimilating new ones. Point him to online resources like dictionary.com and he can self-check his pronunciation, too.
Your son will likely get enough training in phonics at whatever schools he attends, which you note is currently happening in English class. I wouldn't worry about it. As long as reading isn't holding him back, which it sounds like it isn't and won't due to his French ability, it's not a problem for now.
There was a thread a little while ago on word roots, prefixes, suffixes, and etymology. Getting some materials in those areas might help him and cultivate a love of words at the same time.