Outfit for Late May to Early June

Bonjour! 29M, looking for recommendations on what should I wear for a trip from May 27th to Jun 2nd. I assume it's not that hot yet in Paris during those days (high of 20C, low of 10C). I want to fit in with the locals as much as possible. Do I have to bring an umbrella in case it rains? Merci! :)