One should consider that while the French claim to love dogs, they do not love them in their museums(understandable) or in their parks (not understandable).  Having said that, you may be able to sneak a dog into the Tuillery Gardens by trying multiple gates.  The Rodin Museum, on the other hand, will not allow dogs even in the gardens, despite not having signs prohibiting dogs. Paris is strict, dogs are allowed off-leash at both the "bois de vincennes" or "bois de boulogne", large forest type parks on the outskirts of the city. You can also bring your pampered pooch to the park behind the Eiffel Tower "champs des mars", but please bring bags to pick up with, it is a serious 475 euro fine and police are on bikes with whistles ! Almost every bistro, restaurant and cafe welcomes dogs of all sizes. They will usually bring a cup of water.

Cafes and hotels do not seem to have any problem allowing dogs inside, although some hotels may charge a fee per dog per night!  On the bright side, you can go on the wonderful red doubledecker buses that cruise all around the city, stopping at every significant sight.  For 22 Euros, you can get on and off as much as you like for two days and bring your dogs along too.  Highly recommended, as you can plan where you want to go, get your ride there, get off, spend as much time as you want, and pick up the next bus as they come every ten minutes.  They even throw in earphones for a very superficial discussion (more like a sentence or two) about each landmark. 

Air France is a good option if travelling  with dogs. They will allow dogs under 4kg (including container) in the cabin; larger dogs are put in the hold.  You should check out their guidelines prior to buying tickets.Please confirm with any airline before traveling regarding the size of your animal allowed to travel with you in the cabin or as cargo. All airlines have become quite strict recently (as of 2008) and are prohibiting dogs from traveling because of temperature. Also, many passengers complain of allergies and there is typically a dog per flight rule in place on most International airlines.