Re: Meanwhile, back in La France...
The pedant in you might be pleased to learn your pedantry is incorrect. The term "vaccinia" as a formal name for the smallpox virus came after vaccination. Cowpox has the latin name variolae vaccinus. This translates pretty much directly as pox of the cow. The terms vaccine and vaccination originated in the use of cow-derived material for the first of Jenner's innoculations. The term vaccinia was coined much later when the understanding was gained that the cowpox and smallpox viruses were not the same.
By any definition modern or classical the jabs that we receive are both vaccines and immunisations. They are also likely to be widely accepted as innoculations, but they are certainly not variolations.