Tourism can decrease housing supply, making is less affordable for long-term tenants. At the same time it can also increases city and local business revenues. This is a tradeoff that cities should consider and decide where they want to stand.
Of course if you have unbounded house construction policy, than tourism would not effect long-term housing prices much (Though it can impact price distribution in terms of location). But such policy might be impossible in historical city centers such as Paris where buildings have historical value, and are probably one of the reasons for tourism in the first place.
On the other hand, short-term housing, especially through things like Airbnb, can often be offered by people who just have a spare room and who otherwise would not bother renting it out. Allocating this type of housing to tourists might not hurt the housing market by a lot. (Though I do wonder what percentage of Airbnbs actually have such a situation)