The plane dropped him off, then flew the roughly 480km back to Bordeaux, before returning on Monday to pick him up in Provence and take him back home, said the Canard Enchainé.
His alleged usual means of weekend transport, the Dassault-Dornier Alpha Jet, is a light attack jet that in France is mostly used for training purposes and in the Patrouille de France, the country's aerobatic display team.
The flight time between the two air bases which lie on opposite sides of the country is less than an hour in an Alpha Jet, and could be as little as 30 minutes if the plane flew at its maximum speed of 1000 km/h.
Driving between the two points would would take at least six hours and a train trip would take around seven hours and involve two changes.
Using a commercial flight for the cross-country hop would involve flying to Marseille, which would take an hour, and then a roughly 30-minute trip to the general's home which French media said was in Les Alpilles, a picturesque range of low mountains between Salon-de-Provence and Avignon.
Reboul's alleged misuse of military planes came as the French Air Force has been ordered to drastically limit the use of Alpha Jets, which are manufactured jointly by Dassault in France and Dornier in Germany, and other training aircraft due to funding cuts.
Le Canard Enchainé said that the Alpha Jet guzzles around 800 litres of kerosene an hour.
French media estimated that with kerosene for fighter jets costing up to eight times more than fuel for regular jets, the general's weekend getaways may have cost the air force, and French taxpayers, tens of thousands of euros over the past year.
The general, a former fighter and test pilot, was number two in the air force but took the helm as an interim measure last month after the death of his superior, General Serge Soulet.
The Defence Ministry said it had launched an inquiry after "information about an abusive use of air force assets by a senior military official has been handed to the Minister of Defence".
Disciplinary proceedings would be launched if an "abuse of resources" was proven, it said.
The Defence Minister also ordered a report into the use of military jets so she could have clarification on when exactly they can be used.
