Go out of peak season when it's not too hot for travelling.
Pick a site with decent washblocks - some have baby bathing facilities. An alternative is one of those 'blow up' paddling pools - which you can use during the day as a 'cool down' and at bath time fill with warmer water and there's your baby bath.
Don't plan to travel too far - a fractious baby in the back can make every mile seem like ten. Supermarket cafeterias often have special baby meals - and sometimes these are FREE! (Yes, FREE). They'll also give you flasks of hot water or heat up your own food.
Pack familiar things - cot bedding, etc., so it's not too different to home.
Try to get a 'family' site - and you'll meet lots of others in the same position.
We've been camping in France since my eldest was 5 months old - and he's 25 now! The youngest was only 4 months the first time he we went. The first holiday a lovely elderly Dutch couple babysat for us - and I'll never forget the freedom of being able to go to the site bar for a drink! Lovely. We're going back this year with the youngest (now 19) and two of his friends, and the eldest is going to the West Coast of France, camping and surfing, with a party of friends - so we must have done something right!