If you are more into modern art than more classical stuff, you should definitely try the Pompidou Centre (Centre Georges Pompidou)! It has an incredible selection of 'conceptual' art etc, but it's all really approachable and just generally fun! And the building itself is of course an attraction in itself!
I'll second this. Pompidou was my favourite in Paris.
I also enjoyed the Musee d'Art Moderne de la Ville de Paris.
I found the Louvre too big and find the modern art more interesting generally. Depends what you like I suppose