Parisian here. As early as possibly within your available window!
Summer is when construction happens in Paris. Lots of dust, people are grumpy because they're too warm. It's not really hot compared to here, but they don't know that!
If you can change your plans, Spring is so much better. You can buy a baguette sandwich and stroll down the Seine banks amid chestnut blooms... except me. I'm allergic to chestnut trees