Application dates

As for the joint master (application at M1 level):

If the first year is done at ETH Zürich, :
Application dates: November 1st – December 15 (for entrance in the fall of the following year; this window is designed for international students who need a visa);
(see the full calendar on ETH's website).

If the first year is done at École polytechnique:

See the IP Paris admission site

As for the M2 at École polytechnique:

See the IP Paris admission site