Thanks to chrissoup who guessed passionfruit! Passionfruit? In the middle of Paris? It looks like it is technically Passiflora caerulea so a close cousin of Passiflora edulis the "real" passionfruit. And I did brave being yelled at and grabbed one off the vine. My specimen was a little shriveled, but when cut open looked pretty cool. I did taste it, and it was passionfruity, but again, it was getting old so I'll just have to guess the ripe ones are better.
So now to figure out the prize! I know it will be something good...with yummy French sweets! (And Belgian too because I have something delicious in mind.) Now if you would please you big winner, can you email me at parisreally at gmail dot com? I'll make sure to get your package off ASAP!