I think driving is an excellent idea. We drove to the Alps with a tiny baby, and then another time with a 1 year old. The long trips are fine as long as you don't rush. We planned frequent stops when the baby started to grizzle - then we'd stop at a service station, use the facilities and change the baby, get fresh air, a snack, let our older child play in the play area (there's always one of these) and all get fresh air.
We took a large picnic blanket with a plastic back, to roll out on the floor so the baby could stretch and kick around. It was handy on holiday too.
When the baby was a bit worn out, we would get back in the car and the baby would settle and sleep.
We were lucky our oldest was already big enough to sit in the front, so I could be in the back entertaining the baby.
For the older child, we got a holder that hangs over the rear of front seat to hold an iPad, then we downloaded lots of things from Netflix and Cbbc to watch on the way. We also had books, toys, plenty of drinks and some CDs to listen to in the car.
I recommend get yourself a little collection of EUR coins to pay for the toilets in service stations and take some food as I've often found the sandwiches in French service stations are appalling and not child friendly.
If you are using eurotunnel there's a really nice indoor play area the 5 year old will enjoy.
We are going to Disneyland (a week at the Centres Villages nearby) in May with our 3 and 11 year old and I truly cannot wait. Originally we booked it two years ago but of course, covid happened.
Hope you have the very best time, I wouldnt be too worried my experience with babies on holiday has generally been excellent.
Oh final tip - in case the baby is teething take a full bottle of Calpol and some teething powder and a teething thing to chew on.