java.lang.Exception: 401

Did you use any diacritics (accented letters) in your user name or password? Looks like Garmin Connect cannot handle them correctly. Try with a new account without using any diacritics.

Hi trux,

Thanks for your awnser.
Yes i saw similiar post with this trouble explained. But I have only letters and numbers in my user / password :'(

Can you log into your Garmin account on Garmin Connect Web, and into the global Garmin account?

yes ! without any problems !
Maybe it's my phone then :|

Try setting the language of the phone (in Android settings) temporarily to English. Normally it works with the French environment without problems, but it is certainly worth of trying anyway.

OK, I've tried (the app is now in english), but I still have the error.

If you can test it on another phone, try it. What is your phone model and Android version? No Android updates available for your model? You can also try installing an older version of the GCM app from an APK archive (i.e. apkmirror.com or apkssl.com) - older versions may be perhaps better compatible with older phones. 

Sadly I have only one phone. It's an honor 6 with android 6.0. The latest android version available for my model is installed.
I'll try other archives. As a temporary solution, I've used Garmin express on my laptop and it's working just fine !

Thanks for you help !