OK Erik,

I read and read and read and read again your post...
Finally, I think that I manage to understand. I will try to summarize for those who are interested to follow this way:

It's not possible to activate content duplicata with Ventrian (it fails if you have too many articles).
Therefore, do the following:

1/ Do *NOT* enable extra languages when you enable content localization.
2/ Set the culture of every page and every module to Null (in the Tabs and TabModules tables).
3/ Recycle the site and afterwards, activate the extra language.
4/ In the DB, set the culture of all pages that you want to have translated (in my case, all pages)
5/ Recycle the site.
6/ Click "create translation copies" icon that is available for the extra language. The process will now skip all pages/modules that have a NULL culture.
7/ You are done, you have module in both pages, en-US and fr-FR, and you can delete one if needed, etc...

Thanks,
DV FX
PS: I do not know how to link this with Sacha explanation, but that works !