Are we allowed to eat while driving?

Service-public's response: No, the highway code does not specifically prohibit eating while driving. However, this should not prevent you from performing the maneuvers in good conditions.

Indeed, if not prohibited, eating while driving can lead to a lack of control of the vehicle. Article R. 412-6 of the highway code provides in particular that 

every driver shall be in a constant state and position to perform all maneuvers conveniently and without delay

, police or gendarmerie forces may be required, if they detect dangerous behavior, to punish you with a lump sum fine of €35 (contravention of 2^e class).