Already two good answers (François Charles' shop is in the old Galerie Vero-Dodat close to the Louvre; for Duponts shop at the Avenue Daumesnil I'd call in advance to ask if they have any ukuleles to show).
Most shops for musical instruments are in the Rue de Douai and its surroundings, that's close to Place Pigalle.
Then there are the ukulele encounters. Every second Thursday evening there's a Cabaret du Uke at Rue de Mouzaïa, hosted by Phillipe Krouk. The other grand host of the ukulele in Paris, Bertrand Saint-Guillain, threw Ukulele Hui' meetings every first or second Tuesday at the Rue Sambre et Meuse. Best mail them to know the exact dates, hours and places. Their contact adresses are easy enough to find. Even when you can't make it to the meet-ups, those two would be the ideal guides.
Also worthwhile, just 4km outside of Paris, is the workshop of Mike Lewis in Vitry-sur-Seine, who makes Fine Resophonic. He's the only one currently making dobro-style spider bridge ukuleles. He doesn't actually have a showroom, but an email in advance should tell you if a visit is possible.