Those two sentences have different meanings. "Since I was 20' refers only to the year following your twentieth birthday. You were only 20 for a single year. "Since my 20s" refers to your entire decade between the ages of 20 and 29. It is a ten-year period. And no, you can't say "my 20". This doesn't mean anything. By the way...you should have said "I've been wanting to visit France". Present perfect continuous. "I've been wanted" doesn't mean anything (unless you're a wanted criminal that the police are looking for!).

You can't say "since my 20" on its own. You would need to say "since my 20th birthday" if you wanted a construction like that. "since my 20's" implies an unspecified age during your 20's whereas "since I was 20" means the starting point of wanting to go to France started at 20 years old and continued I assume throughout your 20's/30's however old you are now. A correct way to say it would be:"I have wanted to visit France since I was 20/since my 20's" "I've been wanted to visit France" is incorrect. You need to use "I have + past participle" for example: when you arrive in France you could say: "I have waited for this moment since I was 20"

Same meaning

Hi Stanislas, the meaning in both these sentences is the same, but the sentence: "....since I was 20..." would be the one I would use.