EA
The "British validation" mentioned is automatic (requires no paperwork) but has limitations. Art 21(4) renders an ICAO licence issued by another state valid for private flights, except for IFR in controlled airspace.
Unfortunately that means that your FAA IR is not much use for flight in a G-reg in France.
The F-reg issue is that the French authorities require a validation of any foreign licence that is not an EU (effectively JAA) licence issued to an EU citizen. Further, if the holder is an EU citizen seeking to use a non-EU licence, they require proof that the holder is resident in the state of issue. So if you're resident in the UK, they will not validate an FAA licence for use on F-reg. Presumably, since you're not wanting to fly an F-reg it doesn't matter.