Hi Philippe,
Actually mendix make eclipse ready project, hence you can see the option Deploy for eclipse. Now in order to make it compatible with your IntelliJ , you need to do two things 1) check the launch file in the project folder. 2) Check .(dot)classpath file.
From first you can create a sample profile for the same for yourself to run in the IntelliJ. and same with the classpath. Unfortunately I havent worked on IntelliJ :(, Hope this will helps.
Thanks Shubhashish
Current releases of intellij allow you to import eclipse projects. Have a look at:
http://stackoverflow.com/questions/5781137/how-to-convert-intellij-project-to-eclipse
Furthermore have a look at how to connect to the debugger:
https://world.mendix.com/display/howto50/Debugging+Java+actions+remotely