IT WORKED !

I was finally able to send the bitcoins. The solution to the problem was quite simple.

My ballance was not 0.5761188, it was 0,5761188. MultiBit works only if you put a COMMA between the numbers. In Europe (at least in Switzerland) we have a dot "." between numbers, not commas.

It finally accepted 0,0001 BTC as fee (NOT 0.0001 BTC).

Thead can be marked as solved. special thanks to DannyHamilton.