The Versailles gardens are not primarily floral but architectural. They involve multiple copses which contain fountains. There are a few flowers in some of the beds near the chateau, but it is not about flowers. Giverny however can be quite marvelous in May and the Luxembourg Gardens usually has lush floral displays as does the rose garden in the Bois de Bologna. Paris gardens are constantly replanted as the season goes on. April for chestnuts and wisteria, fruit blossoms and bulb flowers; the parks are in bloom in April; in May it is sort of a transition as bulb flowers are done and they are planting petunias and assorted other blooming flowers.
We have been in Paris in May for most of the last 20 years and it is highly variable. We have been there when it is cold and showers a lot (we have rarely had pouring rain all day although in recent years we have had that in October and November.)
but we have had miserable cold Mays in which I was grateful to have packed my silks as I needed that extra layer most days. Other times it has been sunny and temperate. And with climate change it is even harder to predict. Depending on how wrm April is you may still have the chestnuts in blossom and wisteria in bloom -- It is usually petered out. by mid May.
Keep an eye on weather forecases and pack layers and be sure to have a raincoat and waterproof shoes. A light pair of gloves is not a bad idea. I like to travel with only two pairs of shoes and one of them is a lightweight hiking shoe which is water resistant and before travel I always spray them with waterproofing -- the raincoat as well. The shoes won't do for wading through a stream, but keep my feet dry on rainy streets of cities and villages. A lightweight raincoat that can be layered over polar tek, cashmere or a down vest works well to adapt. I always have a pair of light weight pants and a travel shirt that works as a light jacket for days it might be actually warm. It is not going to be hot -- if you are lucky you will have sunny days that are about 70F and perhaps a shower at 2 pm for 20 minutes. If not so lucky it will be 45 F and damp.
We like May because we don't like hot weather. This year we are doing mid April through May and hope to catch temperate weather.