What is needed in addition to the rent money each month?

The address of the apartment is Les Floralies - BatG - Entrée E - 01710 Thoiry.  Make sure to add your name on the mailbox.

Each month you will have to pay the rent of 1250€, it includes the charges (which amounts about 300€ per month).

You will have to pay the electricity monthly or every 2 monthes. In the apartment everything is using electricity, the heating of the house and the heating of the water. http://www.edf.fr
Souscrire un nouveau contrat https://particuliers.edf.com/offres-d-energie/electricite/acces-espace-client-20010.html
Particuliers https://particuliers.edf.com/aide-et-contacts/contacter-edf-54847.html

You need to take a house insurance, to insure any damage you may do in the apartment or you may do to yourself or to somebody else.
I suggest you the insurance company Maif http://www.maif.fr/
The house insurance are available: http://www.maif.fr/particuliers/habitation/assurance/contrat-raqvam.html

Each year the french governement requires you to pay the "taxes d'habitation" which amounts about 500€. It seems to be linked to your revenue. For this, you need to fill your revenue in France by filling the Cerfa paper nr 542.
http://www.impots.gouv.fr/portal/dgi/public/particuliers.impot?espId=1&pageId=part_taxe_habitation&impot=TH&sfid=50

It is your choice to pay for the TV tax, your best bet is to put the TV downstairs in the cave. I don't know how much it costs.
http://www.impots.gouv.fr/portal/dgi/public/particuliers.impot;jsessionid=Q4WRIGFIXDIVDQFIEIQCFFQ?espId=1&pageId=part_redevance&impot=RTV&sfid=50