If you want to pass as a Parisien you will need a small dog...
This is not so practical for a short-term traveler, so why not a small doudou? 
The French doudou is usually carried under the arm leaving the hands free for shopping and snacking... 
Hermes Rive Gauche has a quite a nice doudou sitting in it's window... 
There's an oversize doudou inside Hermes observing the shopping area - this one is not practical for under-arm carrying around... 
BEAR (a Sonia Rykiel doudou himself) loves to browse other doudous... 
Though a doudou does NOT have to be a bear. It can easily be a lapin/rabbit. 
A homard/lobster is a rather unusual doudou one might conclude... 
A rat/rat even moreso - this one is ready for August vacance... 
It now makes sense to me the all the giant chocolate doudous at Easter - this one is at posh Hediard. 
Today Elle Magazine announced Les 'IT' bags de la rentrée
If you have a sac a doudou you can get away with spending less $$...
In future I'll be carrying BEAR under my arm instead of in my bag. Qui sait? I may get mistaken for a Parisian. Then other Parisians will stop to ask directions and other questions I can't answer...