The easiest, closest and most secure solution for your vehicle is to park your car in the Nicetoile shopping centre car park, which is a 5-minute walk from the flat. The car park is open 24 hours a day.
Rue Lamartine, just after the crossing with Spitalieri st.(pedestrian), take the right entrance "Biscara" (pink side ;-)
Park near the glass doors of the Nicetoile shopping centre entrance. You are on floor -1, just below the street.
Take the pedestrian exit on Spitalieri st., cross Lamartine st., take ruelle des Prés, turn right "ruelle des prés" until the entrance to the building (22Ter).
There are degressive rates for several days: consider buying a "pass":