The schools all received practically identical calls between 10:20 AM (1450 IST) and 11:20 AM, police added.
Students at Charlemagne, Fenelon, Montaigne, Condorcet, Henri IV and Louis le Grand schools, all in up-market districts of the French capital, were moved to secure areas while police carried out searches.
Only one suspect package, which could have simply been an abandoned bag, had so far been found, police said.