There is no formal application for Georgia Tech-Europe at the graduate level. Masters and Ph.D students must apply to and be accepted by a graduate program in Aerospace Engineering, Computer Science, Electrical & Computer Engineering, or Mechanical Engineering at the Georgia Institute of Technology, indicating "GT-Europe" as their campus of choice. (note that for the 2022-2023 recruiting season, students may need to select "GT-Lorraine" as their campus of choice.)
Incoming students apply via Georgia Tech's main campus in Atlanta, and after two semesters on the Europe campus, have the option to either complete their degree in France, or request a transfer to the Atlanta campus for their third semester. Students on the thesis track only can spend two semesters in Atlanta and will be eligible for Optional Practical Training (OPT).
If you are currently in an MS engineering program on the Atlanta campus (any major), you may spend a semester at Georgia Tech-Europe by simply requesting a change in campus from "Atlanta" to "Europe."
Visit Georgia Tech's Graduate Studies page for information on starting your application to Georgia Tech.