Well....I disagree. To a certain extent. Pronunciation is very important. I'm not advocating that people try to make their native accent disappear. Your accent is part of your identity, you are charming when you speak English with an accent, and honestly, very few adult learners of English ever get a perfect accent.
But surely you'd prefer this:
I still have a terrible English accent in French, but there are certain sounds which I have worked a lot on. The u for example. Being able to identity this sound means I know if my yoga teacher is saying dessous or dessus (under or over) and I don't embarrass myself by saying cul instead of cou (butt and neck.)
In the next few blog posts, I'll give French-speakers some tips on pronunciation and what to practise.
Meanwhile I will leave you with a South-African rugby player who has managed to get an excellent French accent. (Thanks to my student Fred for this video.)