score:5
Free2move has some Citroen Ami as part of their fleet of cars in Paris. You might have to walk a bit to find one as I have the feeling the Citroen C-Zéro are much more common.
I believe you can even register with their UK branch, completing all necessary formalities (uploading a driving license, taking a verfication selfie) and use the same account while you are in Paris. I have not tried this particular combination (Free2move, UK -> France) but I did complete their registration process with a foreign license and I have used a competing services (ShareNow) across several countries with one account so they are definitely open to non-residents (ShareNow only has Smart EQ fortwo or forfour in Paris so it is not a good fit for your purpose).
The rental prices are not that attractive if you want to keep the car several hours or go to the countryside but it is in principle possible. You can in any case easily go for a 30-min test drive in the city for €10 or so and drop the car wherever you want inside Paris. The small size is definitely a big plus when it comes to finding a parking spot.
Note that since the Citroen Ami is not classified as a car in France, you are not allowed to drive one on the Paris ring road (boulevard périphérique). In spite of the fact that it can technically be driven without a driving license, I also believe Free2move requires one from its customers (possibly for insurance purposes or because they won't restrict your account to a small part of their fleet).