The TV licence fee is payable along with taxe d’habitation (this is still applied to second homes) by all who are eligible to pay this tax and have a TV or similar device, such as a DVD player equipped to receive TV.
It is possible you were exempt from the taxe d’habitation if the home was being renovated and was not furnished or habitable.
The main issue now is whether or not the home is equipped with a TV. If not, no fee is due (having a computer that you can watch TV on over the internet is not counted).
As far as it being a second home goes, this is relevant only where someone’s main residence is also in France and equipped with a TV, as people only pay it once per tax household even if they own multiple properties.
Where someone owns a second home in France but is not a French tax resident, the fee is still payable as it is their only French home.
If you make a French tax declaration, cross box 0RA to continue to opt out of paying the fee due to not having a TV.
If you do not declare because you are non-resident and have no French-source income, then you may want to check with the tax office to make sure they know not to levy it.
We have a dedicated helpguide on Owning a Second Home in France. Order at the helpguide section of connexionfrance.com