Boeing100,
Please be aware that National Authorities are responsible for issuing Language Proficiencies and (most) will not recognise Proficiencies tested and recorded by another state.
The UK CAA will not recognise your English level 6 from your French issued Licence.
This is not a problem: Any UK Examiner can issue you with Level 6 English (provided you are) following an assessment (10 minute chat, or as part of a Proficiency Check).
Ensure you get your English LP recorded, either on the standard SEP Renewal Form if applying directly for a UK Licence, or on the stand alone LP form if applying first for renewal of your French issued one.
Note: If you have French Language Proficiency noted on your French issued Licence, I am unaware of any method of getting the UK CAA to recognise this.