I'm having a similar problem with my DC's, although we are an English speaking family, but they are in French school. I read the stories in French, but I comment on them in English and discuss them with him in English as I personally don't have the vocabulary skills to discuss it in French. If there are words we don't understand, then we get the dictionary out and learn them together, so far it seems to be working. I don't think discussing it in English is a problem because the story was read in French but the discussion we're having shows that they understood the context of the story in a second language. DS2 is in MS and he absolutely refuses to speak any French at home, it's English only, although his teacher tells me he understands and uses French at school so I presume he's distinguishng between the two different places and using the two different languages.
The problem we are having with spelling is DS made huge progress over the summer holidays with his English reading, but I taught him phonetically and now he's trying to apply the same rules to French. So he has absolutely no problem with words like ami, un, la but huge problems with de, des, le etc. We've had to discuss the different sounds of the French alphabet and I used the names of the children in his class and how differently their names would be pronounced in English because of different letter sounds. I think he understands and we approach the reading now by saying tonight it's French or tonight it's English. I'm hoping it's something that he will overcome naturally as his reading is more established in both languages, but I must confess until this week it was a problem I hadn't foreseen.
I think to try and use the French sounds when reading French words and the English sounds when reading English words that way they will come to recognise the difference.