Lightning struck the Parc Monceau, in the west of the French capital, during a storm on Saturday afternoon.
The children, who suffered burns, have been taken to the Necker hospital.
Torrential rain also halted play at the French Open as defending champion Serena Williams was about to start a match against Kristina Mladenovic.
The children were celebrating a birthday when rain began to fall, a police source told AFP news agency. They sought shelter under a tree when lightning struck, the source added.