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You might already be doing this, but imitating phrases might help? Sometimes how one word flows into the next also contributes to the sound. For example (in American English), if you say "want to" quickly (fluently), it sounds like "wanna." Also, make sure your input is consistent. American English and British English sound different, so don't mix the two.

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Great job.

If you ask me, the only thing that matters is correct pronunciation. I think us having different accents is a beautiful thing - especially a French accent in English. The trick is finding the balance of correct pronunciation (being understood) with your accent. I've found French natives to be unnecessarily critical about their own accents. It is not as if all anglophones sound the same - Americans, Canadians, English, Irish, Scottish, Welsh people, Australians, Kiwis, South Africans, etc. all have different accents.

I once met a French woman who spoke English exactly like me (an American), which she worked really hard for and was very proud of. As impressive as that is, I found it sad (and again, unnecessary) that she wanted to entirely erase her accent. But I suppose we all have different reasons and motivations for doing things.