We're planning on spending a few days in Castellane next May. My husband would really like to get a chance to take a rafting trip on the river.
Problem is I'm not a good swimmer.
Has anyone taken a trip through the Gorges and do I need to worry about it? I will of course be wearing a life jacket.
Just want to know how turbulent the waters are.

I've been researching this for our trip next May as well. I found this link:
http://www.provenceweb.fr/e/groupes/verdon/eauvive.htm
At the bottom there are links to several companies that have descriptions of their different trips, I am sure you could find something that would work for you. Just make sure you check the description of the rapids so that you are staying away from the upper class rapids. On a number of trips the minimum age is 8, I am sure you can do something an 8 year old can do, even if you aren't a strong swimmer.

Will May and spring have more rushing water than later in summer?

I would assume you would have faster (or at least a higher volume of) water in May due to the spring thaws. However, the water releases in this area are controled by a dam, so its not the same as being on a wild river.

Thanks for the link. Looks I might go for at least part of the river trip.
My husband promises to save me in case of any unfortunate happenings.

I did a canoe in August once with my young son - we were inexperienced and did tip over once - yes life jackets and a bit of a problem righting the boat but i do not think these trips are dangerous.