No one can tell you with any sure accuracy the type of rain you will have.. you will be lucky if you know the day before if you listen to local weather ( and understand French).
I have been in Paris in every month from May thru October.. it has rained in every month.. sometimes heavy.. sometimes light drizzle. .and then within 1/2 hour it can clear up( this is especially true of summer showers.. one time in August the rain was so hard it practically bounced off the sidewalk and hit you in the face,,lol..
I have roasted in May.. been cold in July.. it happens.. I have hit heat waves.. and cold waves.. its really weird weather in Paris..
Take a light rain jacket no matter which month you go. Take a sweater or similar to layer underneath. I bring two pairs of shoes.. plus sandals for summer.. if its wet I can alternate dry and wet shoes.
I always bring a small umbrella.. I hate hats .