Thank your for you help.
But I'm not sure my question is clear ;-)
Basically, what I want is to create a bilingual site (French and English) from the same Theme template.
And I want to offer my users the opportunity to switch from the french to the english version of my site (or vice-versa) from a simple click on a link, or a button or anything else.
And as per the Admin point of view, I would like all my site pages (french and english) to be available in the same WordPress Theme Dashboard.
But I think it might not be possible.
I might have to create two identical sites, one in french and the other in english, and ad the button or link you are referring to in your previous answer.
Am I right ?
Thx again for your help and consideration.