I don't know anything about the French rental homes market but in the USA there's ample headroom in lessor profits to take a haircut without triggering the second-order effect that you hypothesized. Landlord income as a share of GDP (again, in the USA) stands at a post-War high, having increased 15x from its low around 1990.

Landlords have a huge and largely unearned cashflow and the thing about taxes is it's best to try to raise them where the money is.