You can call GLContext.getCurrentGL() to get the GL instance but your method must be called when the OpenGL context is current. Look at the source code of Ardor3D JOGL renderer to see how I use it.
Why not using GL2ES2 and GL2ES1 where it is possible so that your code has a chance to work with OpenGL-ES too? Your source code would be easier to read if your variables weren't named in French and without respecting Java code conventions. Finally, the official JogAmp forum is a better place to ask questions about JOGL.