Provence in late April and French school holiday

Yes. That’s prime time to head toward some sunlight after going through winter for Northerners. Forty years ago we were teachers in the Paris region and ran into crowds in Provence. Of course, infrastructure, such as restaurants, hotels, and parking, was much less developed then.

Only to some extent. School holidays are staggered so no more than 2/3 of the country is on holiday at the same time. And April is otherwise not a big month for travel in other European countries so you won't have that many European tourists.
In my experience from the past few years, April is still pretty quiet in coastal Provence. And the crowds spread well over that fairly large region.
One thing to be careful about is traffic around Easter weekend, but that's about it. Train tickets around that weekend should be booked early, too. Otherwise there's nothing that should stop you from going to Provence at that lovely time of the year.

Personally, I'd be more worried about the winds during the spring. I literally crossed Provence off as a spring destination because of Le Mistral. Having crazy winds for three days of, say, five in the area would be a waste. I visited in September and it was still quite warm. I think early October would be perfect - both for weather and crowds.

Regarding Mistral, I lived in Marseille for 2 years, and frankly, come March it is not as annoying as in the winter. It is a cold wind (to me, it does rule out Provence as a region to visit between Christmas and end Feb), but it gives beautiful skies. By Late April, Provence is usually very pleasant.
By the way, Mistral can happen even in high summer.

Thanks everyone!