TLDR: Yes, when your second home is made available exclusively to a third party. To qualify for the exemption provided for by Article 1391 of the CGI, the property must be occupied by you as the owner or usufructuary. This rule applies even in the absence of a lease.
Conditions for the exemption
You must be over 75 years old on January 1 of the tax year, and your income for the previous year must not exceed the threshold provided for by Article 1417 of the CGI.
The exemption applies to the property you occupy. It may also apply to your second home if you meet the required conditions and occupy it as the owner or usufructuary. The fact that you already benefit from the exemption for your main residence does not, by itself, prevent you from benefiting from it for your second home.
Exclusive availability to a third party
If your second home is made available exclusively to a third party, it cannot be considered to be occupied by you. It therefore cannot benefit from the exemption provided for by Article 1391 of the CGI, even if no lease has been concluded.
The removal of the cohabitation requirement, applicable to tax assessments established from 2023 onwards, does not change this rule.
Age is assessed on January 1 of the tax year. The income taken into account is that of the previous year.