I think it's better to say, in the first sentence, "I want to go to France to study French.", because when you use the verb go you usually ask 'where?'. The verb go usually takes an obligatory adverb because go is a verb of movement and needs an adverb to be completed. So you can also just say "I want to study French in France." if what you mean is studying in French in France. Obviously you can't study French in France if you are not in France.
Regarding your second sentence I think you can't use the sequence auxiliary verb + main verb + modal verb + main verb, so you have to think what you really want to mean with that sentence and rephrase it. The verb 'don't want' is expressing you don't desire something. In my opinion it's better to say 'I don't like going to bed early.' I'm not completely sure of my thoughts in this sentence though.
In the third sentence I think it's better to say 'Do you want to practice English speaking later?' like if 'English' were an adjective modifying 'speaking'. Other ways to say it and that I think are better are 'Do you want to practice English conversation later?' and 'Do you want to practice English later?'.
The 4th sentence is correct. Although you could only just say 'Do you want to play the game now?'.
Take into account that I'm not an English teacher but an English student.
Hope my post helps you.