The key fob is not a big issue, £5 tops from t’internet. We had the same issue, trawled all round the French car parts companies to no avail. Replacement key fob from t’internet,swap the button half, job done.
I’d say £2k was a good price for one in good working order and FSH incl cam belt. Tyres are tyres, they need replacing every so often anyway, so I’d not include them in the valuation.
If the seller can prove the cambelt has been done then, provided everything else works, it might be a good deal. If the cambelt can’t be proven then that’s a bit of haggling room.
Check all the electric windows, lights, wipers, aircon, stereo, cruise control etc. oil filler cap, dipstick, coolant system, diagnostics system
I’d avoid a big car if she’s still learning, C4 is plenty big enough