Not if there isn't significantly more demand that supply. Rent control has worked well to mitigate housing issues in Paris during the last few years. It didn't solve everyone's problems: more and more students are moving to the close suburbs, and getting an apartment can be highly dependant on whether your landlord deems your income stable enough. But it has also prevented rent escalation - which we're currently seeing now that a court has repealed rent control [1].

[1] https://www.lemonde.fr/logement/article/2017/11/28/apres-lil...