There are so many beautiful parks in Paris, such as Jardin du Luxembourg or Tuilleries as mentioned above. Any google search will give good suggestions.
http://www.timeout.com/paris/en/things-to-do/the-ten-best-parks-gardens

Don't forget to buy those little white flowers they sell on all the street corners on May 1st!

Day trip to Dinseyland Paris

Père Lachaise Cemetery. I was there one May 1 years ago and that was about all I could find that was open. Of course things could be different now.

Go to the Tuilleries. There are playgrounds, places to sit and eat, trees to rest under and watch the world go by, walking to do, fountains to see.

Or go for walks generally.

First visit. Trying to plan itinerary but everything seems to be closed that day. We will be traveling with two kids ages 8 and 3 and will be in Paris for 10 days. Should we leave Paris that day? If so, where should we go. Thanks in advance! Traveling the first week in May.