The table below summarises the plug types, voltage and frequency of electrical current in both France and Luxembourg.
|Plug Types||E||C, F|
|Frequency of electrical current||50Hz||50Hz|
France uses Plug Type E.
The voltages found in France (230V) and Luxembourg (220V) are not exactly the same, but the difference is tolerable, so you should not need a transformer.
The frequency found in France and Luxembourg is exactly the same (50Hz). Timing devices and appliances that use motors will function as expected under this frequency.