The Falcon 7X plane, which is decked out in a special République Française design, was taking the president to an appointment in Ariège, close to the Pyrenees.
When the problem was detected on Tuesday morning the plane was forced to land in Toulouse, causing the president to be late.
"It didn't bother the president too much," said an adviser, reported daily newspaper Le Parisien. "He was talking to representatives from the agricultural workers' association."
A second Falcon 7X was commandeered to fly the president back to Paris after his visit while the first remained in Toulouse to be repaired.
France's president also has a specially designed Airbus 330, nicknamed Air Sarko One, at his disposal.
The second hand jet carries anti-aircraft missiles and has been refurbished with a double bedroom and a conference room. The plane is reportedly also kitted out with a pizza oven.