Family hotel in Paris, preferably near a park?

The Gardette Park Hotel may or may not have adjoining rooms.

I'd stay in the Hotel Residence Henri IV, where you'll have the benefit of a kitchen, as well as two bathrooms. Because you'll save money while cooking - and there's a market just steps away.
http://www.residencehenri4.com/en/

Or, the Hotel Saint-Louis-en-Isle will fit the bill. You'll have a single room all to yourself, and there is a park on the Eastern side of the island. Or, you can go over the Pont du Sully bridge to Place de Vosges. All have playgrounds.
www.france-hotel-guide.com/en/40422-hotel-saint-louis-en-l-isle-paris-en.php

Hotel des Grand Hommes and its sister Hotel the Pantheon hotel are located ( of course ) right beside the Pantheon .

A short walk down the street and you are at Luxembourg Gardens , a wonderful park for kids !!( and adults ) . There is a outdoor cafe on the grounds and they sell ice cream , a great playground , and a pond that you can rent little sailboats that kids push around with long sticks . There's sometimes music in the park , and lots of room to just relax !

Another vote for being somewhere near the Luxembourg Gardens. Your grandson will thank you. The parents will thank you...

Agree w Pat and Nigel, the playground at the Luxembourg Gardens is amazing. The best one in Paris afaik. The small entrance fee is well worth it.
It is located at the south west corner of the park so a hotel by the Pantheon would be a fair distance to walk, appx 1 mile. You may want to look for a hotel closer (and likely less expensive than Pantheon area). The closest entrance to the park, closest to the playground, is on rue d’Assas (x st rue Vavin) in the south west corner of the park. This will be the 6th arrondissement. Get a very good, detailed map of Paris which will help as you research hotels. There are many in that area.
Have you tried Booking.com or Hotels.com? Don’t have to book through them but very useful in finding a hotel as you can use filters to narrow the search based on what amenities you’d like. And you can read the reviews.