There are several subspecies of tiger. There are three subspecies that have gone extinct. This is a picture of a Siberia Tiger also known as an Amur tiger.

It is my guess this is the tiger that have been seen near Paris. The other subspecies lives in more tropical areas of Asia and far more east and south. This particular species could migrate east from Siberia. It is a long trek, but, considering this species thrives in snow and the cold, this is the most likely to have walked a great distance to insure it's survival.

If this is a young tiger he is a lone male that has been forced from it's normal habitat. That is more normal than one might think.

If one recalls in 2010 there was a huge fire in Russia that killed 50 thousand people. The fire would also be a threat to any Siberian tiger that might have been living in that region. This tiger lives in the farest east of Russia, but, with habitat destruction and pure survival of a young cat could push it east into Europe.

This is a more mature Siberian Tiger. It doesn't matter what species of tiger might be surviving in and near Paris, it is an endangered species. 

The tiger is most probably hungry. It's usual prey include horses, cattle, pigs as well as wild deer. If the tiger continues to be elusive a trap with an animal within it's normal diet would likely draw him or her in. I would be surprised if it is a female.

When looking for this tiger, check the trees, too. 

Competition (click here)

As tigers compete with humans and industry for land, they find less and less to eat. Local people hunt the same prey as tigers do, pressing tigers to resort to domestic animals and, on rarer occasions, even humans. (Tigers are one of only two animals–the other is the polar bear–that are known to stalk humans.)

I know this sounds glib, but, if he had to be alone in the wild and wandering for habitat, I am glad it was into France and ultimately Paris. At least he will survive the hunt for him. I am also not surprised he was seen by people at this point. Tigers are scared of unfamiliar activity. He has probably used his instinct to survive to this point and avoided being seen to this point.

There is another less romantic notion of where this tiger came from. He could have been a pet and turned loose when he began to long for mating and the hunt. Tigers will remain passive and dependent for awhile, but, as soon as the tiger is capable of hunting it will become aggressive and unfriendly. I doubt the owner will voluntarily come forward, but, asking him or her to come forward might give ultimate handlers a clue to the tiger's behavior.

The reason to know whether this was a domesticated or wild tiger will provide insight to where he should live. Either maintain him/her in a zoo or return the tiger to the wild. If it was a pet the idea of survival in the wild might be unrealistic.

I can fully imagine a French citizen finding a way to protect a least one tiger from demise. It is possible if the tiger was a pet, it was conducted out of compassion for the species. 

If a pet, the owner may have been attempting to return it to the wild without much information or resources to bring the animal to east Asia. If it is a pet, it could be any of the subspecies as well.

Good luck.