The blast occurred on Wednesday afternoon at the Samara parc near Chaussée-Tirancourt in the Somme département, about 150 kilometres north of Paris.
School pupils on a field trip were attending a blacksmith's demonstration at the time of the explosion.
All of the 14 children were taken to a local hospital but escaped with only minor injuries. Most of the injuries are understood to be burns, reported local media.
The blacksmith, however, required surgery after a metal bar pierced his leg.
An investigation has been launched as to what caused the explosion, but the Le Parisien newspaper reported that some kind of shell had been thrown into a fire, causing it to explode.
The paper noted that the accident could have been much worse, as the school had sent a total of 420 students to the theme park.
The park recreates ancient civilization, including reenactments and reconstructions for the visitors. It also plays host to a botanical garden.