Bristol blue always an attractive colour. Sorry, no idea as to the authenticity of this as a pressed piece intended to be tumbler - the patterning looks vaguely familiar but that might just be a guess. For whatever reason, of all the pressed examples in John A. Brooks slim offering 'Glass Tumblers 1700 - 1900', none is blue - in fact he doesn't show any coloured pieces at all. IMHO, the rather narrow plain rim at the top might rule it out as a tumbler - what's it like if you put the glass to the mouth for drinking? Often, pressed tumblers had thick bases which were thinner toward the centre (of the base) - something to do with the plunger possibly. With pieces of suspect age, it's sometimes an indication of genuine period if the relief diamonds show some damage - if they're too good to be true, then it probably is - and a bristol blue tumbler that was in excess of a century in age would be valuable I'd suggest.

Sorry this is of no real help.
What in particular makes you suggest French?