The Ecole Polytechnique is located about 20 km south of Paris.
For accommodation nearby the university there are several hotel options near the train station in Massy, which is easily reachable from both the campus (15 min) and from the center of Paris (45 min):
There are also several hotels near the Antony train station, which is slightly closer to Paris:
More options can be found on booking.com, e.g., searching for Massy-Palaiseau Metro Station
For those wishing to stay in Paris, we leave you to explore the many options available. To reach the campus by public transport, it's advisable to stay near the RER B train line. The commute to the campus can take about an hour.