justineparis

Do NOT rent a hotel room as a triple and figure you can throw a kid on couch or floor, especially in Paris.. they will turn you away unless they have a more expensive quad room empty that they will put you in and charge that price
Hotel rooms are sold by room occupancy.. a double or twin room is always a maximum of two people.. a triple three.. etc.. exceptions may be made for infants.. but you still must notify hotel that baby is included.

There is a list of hotels on tripadivor.com Paris forums that are for hotels with Quad rooms.. they are not the easiest to find oddly.

As for renting a gite.. depending on your moving about , I don't consider it worth it for 3 night stays.. ( and obviously no gites in paris. )

Citidines are a chain of aparthotels in paris.. you can find a room for four(usually a one bedroom and a sofa bed) and with small kitchenette.. will save money that way by having breakfast and snacks in at least.

PalenQ

In busy seasons I think gites in popular places would not even take a short-term three-night rental. The longer they can rent it for the less the hassle.

PalenQ

or taking the ferry from Portsmouth to Honfleur, then doing a driving tour before going to Paris>

Or to Oustreham by Caen -right near D-day beaches area if going there.