It depends entirely how it “competes” with the prevalent variant in France - which is the UK variant at present. It is not clear whether it is more transmissible than UK variant so it might remain at quite low levels in both countries.
Do you mind! - the UK govt would like this to be called “The variant first discovered in Kent due to world beating detection”.
I assume this is a combination of UK govt pride and not wanting to be blamed - or stupidity.
The UK govt does seem to continue to refer to other variants by the name of the country that they were initially discovered - seems a, little inconsistent which is a great surprise.
I’ve posted previously that tagging variants with geographic areas is not all that desirable, for lots of reasons.
But if I said “the B.1.1.7 variant” no-one would know what I meant.
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Why don’t they do it like hurricanes and give them names…
They have, Kent, India, Brazil , China 
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