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Antoine, you asked:
"ONE QUESTION : Are there other different theories currently being the source of either Astronomical or Nautical Almanacs in other countries ?"

If you mean government-issued, printed almanacs, then almost certainly not. But there are lots of almanacs around, if you count non-government digital products.

Also, the idea that the French BdL analytical theories are somehow different from the JPL integrations is really an illusion. They are numerical "fits" to the same data (for a given run of the integrations, that is). The form taken by these BdL fits is useful for certain specialized areas of celestial mechanics analysis, but as far as generating the positions of astronomical bodies for some instant of time and producing "ephemerides", there's really no difference at all. The positions of the major celestial bodies in the Solar System can be treated as "known" quantities. You can tabulate them in a database once and for all and then use whatever look-up procedure suits you and satisfies the level of accuracy required for your application. That might be as simple as linear interpolation or much more complicated, but it's only a question of algorithmic efficiency and available memory. There's no science in it, just economics, IF the output of the system is the positional data itself (as opposed to other sorts of celestial mechanics analyses which I alluded to above). The only real unknown for the positional data is the exact orientation of the Earth in the future and in earlier centuries. In other words, you only have to worry about delta-T. For the major planets and our Moon, everything else is finished.

By the way, are you familiar with Aldo Vitagliano's "Solex" software?
http://chemistry.unina.it/~alvitagl/solex/
The interface is a bit old-fashioned but the output is impressive.

-FER