You don't need the maintenance logbook, and I'd be wary of regularly carrying that in the aircraft anyway.
You must carry:
- Cert of Registration
- Certificate of Airworthiness
- Aircraft Radio Licence
- Insurance Certificate
- Anything else your state of registry or CofA requires (e.g. N reg does require a POH. Private G Reg does not)
For yourself you need:
- Pilot's Licence
- Aviation Medical certificate
- Radio Licence
- Passport (of course)
- Not essential, but I try not to forget my Euro medical card.
You must also carry a copy of the Interception Procedures to satisfy French requirements (CAA Safety Sense Leaflet 11 will do the job). (Addition edit to clarify detail - it's a UK requiirement for Int'l flight too, of course.)
Not paperwork, but don't forget that you also need an appropriate 406MHz PLB or ELT. GPS model is necessary.