If you don't have the required paperwork completed and signed by the owner whose name is on the CG, together with all the other items required, dated less than one month before you apply to register it, they will not be accepted.
This will probably only be possible if you are buying the car directly from the person whose name is on the CG. If the transfer section of the CG has already been completed, or the CG crossed and dated as sold to someone (e.g. a UK dealer), you can't register it in a different name.
Details of what is required are here:
If the correct documents are not available, you would probably have to register the car in your name in the UK, which I think requires an address there, then register it in France when you bring it here. Registration here may be simplified if you produce the originals or copies of the French documents.
On some great and glorious day the plain folks of the land will reach their heart's desire at last, and the White House will be adorned by a downright moron.
H. L. Mencken 1880 - 1956
Some may not like his views, but what a prediction!