The first of three French planes sent to evacuate European citizens took off from the capital, Niamey.
The coup has prompted demonstrations against the former colonial power, with the French embassy coming under attack.
However, France says it has no plans to repatriate about 1,000 French soldiers stationed there as part of efforts to counter Islamist militants.
Germany has urged its nationals to take up France’s offer to help other Europeans and Italy is also organising a flight.
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