OK, maybe I found it : in Project Manager, right click, select "Project Tree" / "Edit Files types & Categories"
In the dialog box, select the category "Sources" and add "*.c++".
This will be enough to make CB recognize the file and compile it when building.
Furthermore, to enable syntax highlighting for these files, go in "settings" / "editor". Click on "Syntax Highlighting" category, select "C/C++" and click on the button "filemasks".