Thanks to Jeff Yang for his interest in my problem!
I have - or for the most I had - checked all parameters he suggested.
I hinted since I was able to access to my gmail adresses that the problem was Bouygues mail server.
I etablished a web discussion with Bouygues support. The fact I know is that Bouygues is not eager to provide a great support to their mail server. I didn't get clear answers. But at a time I have been able to access to my maibox from Outlook. I hint they modified some parameters.
Now all is correct!