Study the IPA a little bit. Gain an understanding that we really don't have 'accents'. We simply use a range of vocal sounds to produce speech.
The amount of noises our vocal organs can make is pretty big, but by the time we hit adolescents we have stopped using a large number of them. I.e. Each language uses a subset of the sounds, and the speakers tend to lose the ability to pronounce the other sounds.
So when you say you have an American accent. What you are really saying is that you have lived your life accessing the sounds that the Americans use, and hence you have lost the ability to access many of the french sounds.
Good news ! You can recitify it with practice, just recognise that you are teaching your vocal organs to produce sounds that they have probably not pronounced since you were a baby. Practice practice practice.
1. Practice practice practice. (Check out Youtube for some great lessons on pronunciation).
2. Don't be afraid to exagerate. As you improve you will lose the exageration.
3. Be aware that the subset of sounds used by your target language will sound foreign to your ears. I know that when I speak French I quite often feel like I am just gargling. But that is the french language, it has loads more nasal sounds then the English language.
