The bolt hit the Parc Monceau in the north west of Paris on Saturday afternoon.
“There are currently 11 injured unfortunately, 10 children and an adult who was accompanying them,' Vincent Baladi of the local authority told iTELE television.
Local media reports suggest the children were at a birthday party when the thunderstorm struck.
Fire officers were unable to provide any more immediate details of the accident, which happened at the Parc Monceau in north-west Paris in the afternoon.
Despite warm and sunny weather in the morning, Paris was hit by thunderstorms for much of the afternoon on Saturday.
Much of the rest of France has also seen storms on Saturday.