The woman in the following video, Amy Walker, is an actress, writer, singer, and dancer. She amazingly imitates 21 different English accents from around the world.
After I watched the video, I was impressed by her performance and ability to mimic (copy) the various (different) English accents. I was also fascinated by the native-English accents that exist in North America and the United Kingdom.
My trainees and students often ask me if they have a good accent. I am surprised to hear how they degrade (humiliate, reduce) themselves because they think their accents are horrible.
We all speak English, but differently. Our accents add charm and character to the language.
My answer is that I think their native French or Asian accents add personality to their English communication. In my opinion, the most important aspect of their English is to be comprehensible. I do my best to reinforce that point during my English lessons to break their negative complexes and increase their self-confidence.
If you articulate, people will understand you. Do not be afraid to speak and enjoy the language!