I'd definitely recommend the British museum as well, I could spend a week there! Personally I found the Science museum to be geared a bit too much towards children, so I doubt I'd visit it a second time. One of the coolest experiences for me and many people I know was the London dungeon, so if you're interested in such things you should definitely check it out. I don't know if you're planning on riding the London Eye, I didn't really think it was worth it, but again, that's just my personal opinion. If you like shopping, Oxford street is great though also kind of expensive.

Would you like some company of local people to guide you?

The good news is that all the museums and art galleries are free. My favourites: the National Gallery; the British Museum; the Natural History Museum; the Tate Gallery; the Tate Modern; the Science Museum. The bad news is that public transport is (as I understand it) a little more expensive than in France. However, you can buy a weekly or monthly pass which will allow you to travel within London reasonably cheaply, but if you want to travel outside of London then it might be a little expensive. Hope you have a good time.