Would you be renting in France, and if so in which part? For the passport, just go to the DEFRA website. Going to France is easy peasy, returning is more complex with the dog. You need to insure you get the microchip and rabbies jab done soon as you need x months between jab, retest, and being able to travel (can't remember off hand, must check).
I would also recommend travelling via the Tunnel and not ferry, so the dog can stay in the car with you- and won't even notice, instead of having to stay in the car in the hold, which can be horrendous in bad weather. And on return, you will have to visit a French vet (from top of head, but again, regs changed recently, so must re-check Defra site) no less than 48 hrs before or max 72- and s/he will have to administer a vermifuge (you can't do it yourself) check the dog for good health, the microchip and jabs, + enter the vermifuge, stamp and sign (must be done in passport- we witnessed a lady being refused travel because it was on separate sheet of paper). You then have to allow time to go to Pet Check just before the booths at the Tunnel- and go with your dog where they check, again, that all is in order I(and they are real sticklers- if you are even 30 mins out of sinc, you have to wait or be turned away).