A funny anecdote was when I was working with a guy name Jean-Nicolas and all the Québécois people called him Jean-Nic. That was very funny to the French guys hehe
Obviously they're not different languages - I was a bit exaggeratory in that regard. And I do understand both, in as much as I understand either. French is my third or fourth most proficient language after English, Spanish and maybe German, but I never get to use it (or German for that matter).
The two are however different enough in some pronunciation and idioms that we ultimately had to do a second localization to support both. And the differences reported to us ran the spectrum from simple things, such as how to correctly pronounce the (cardinal) number 1 (a cleaner "un" compared to what sounds to my ear like "arn"), to the longer phrases one might expect to hear in a voicemail prompt. Ultimately our translation department got things ironed out, but it was a (somewhat amusing/bemusing) learning experience for us.
I have another response in this thread about the origins of the Parisian accent (because it really is a new invention) compared to the Québec accent.
Also in Martinique, they speak with a less sing-songy accent than they do on the mainland.
I personally enjoy all the variations of my language, and especially appreciate the language that is 'of the people'.
No, just no, they aren't and I can speak both.
I don't know if you are a native speaker, but It's tiring to have your own language (or 'dialect') explained to you.
For what it's worth, France has dozens of regional dialects as well.