I've learned to write x the way this post says (two mirrored c's) but I don't understand what you mean by "independence days". We don't have one in France anyway.

"Countries with independence days" aka former colonies.

Well I understood that much, but I'm not sure what link it could have with the shape of the x, especially since the English don't do it the same way as India.

It may depend on age - Marion Richardson used to be the standard for cursive teaching in England and that uses two-cs style.