There are a couple of storage places right across from Pompidou.
Châtelet Les Halles - Centre Pompidou Storage Spot
113/119 Rue Saint-Martin, 75004 Paris, France
Online reservation required
And nearby:
Stow your bags
Centre Pompidou | Notre-Dame
8 Rue Nicolas Flamel, 75004 Paris, France
The Stow Your Bags is a prearranged place with lockers that are all over Paris.
Places like Nannybag are essentially Viator style resellers for actual vendors and find and arrange it for you. In Paris it is easy enough to find the actual places because they are all over.
My only advice is have in mind what you want to keep with you and drop off before you get there so you can pull your daybag and go without unpacking the luggage store. With that many people I would definitely book ahead to make sure there's space set aside for you.
Have a great trip, Paris is an amazing city,
=Tod