The ruling by the court was a first on the specific issue of religious beliefs versus school rules where sport, in this case involving some exposure of the body and changing of clothes, is part of obligatory activities.
Schooling, including sports, overrode religious convictions, notably when the school sought to address the couple's concerns by offering to let the girls wear burkinis - full-body swimwear - and change into it without boys present, the court said.
The case ended up at the rights court, based in the eastern French city of Strasbourg, when a couple of Turkish nationality fought a Swiss decision to fine them 1,400 Swiss francs ($1,380) for failure to respect schooling rules.
The Swiss authorities fined the couple in 2010 for refusing to send the two girls, born in 1999 and 2002, to the swimming lessons. After a challenge in the Swiss courts, the parents turned to the European rights court.