Configuring earphone

I believe your hardware is problematic. I have used Trisquel on three different laptops and connecting the earphones has always muted the speakers.

The temporary solution would be to mute the speakers from the output tab of the sound preferences (in the System/Preferences menu). Notice the drop-down menu at the bottom of the window.

This should be an audio chipset-specific issue of the ALSA(Advanced Linux Sound Architecture) sound system. There should be a command to toggle mute/unmute the speakers but I cannot help you with that because I does not use ALSA. I recommend you to try out the OSS4(Open Sound System v4) as an alternative. It also comes with some benefits (such as better sound quality). You can read more here:
https://en.wikipedia.org/wiki/Open_Sound_System
https://trisquel.info/en/wiki/installing-oss4-trisquel-40

Note, that the official (Trisquel's) documentation is a bit outdated and inaccurate so here's my own one:

Open Terminal (press [Ctrl]+[Alt]+[T]), then follow:

To INSTALL OSS4 on Trisquel 4.0(+):
$ sudo su
$ apt-get update;apt-get install oss4-dkms oss4-gtk linux-headers-generic linux-image-generic libc6-dev
$ dpkg-reconfigure linux-sound-base # Select OSS
$ xdg-open https://trisquel.info/wiki/installing-oss4-trisquel-40#toc4
$ FILE=/etc/pulse/default.pa;cp $FILE $FILE-old;gnome-text-editor $FILE # Follow step 4
$ ossmix vmix0-src OFF # This will avoid low quality output.
$ reboot # This will RESTART your system!

To REMOVE OSS4:
$ sudo su
$ apt-get remove oss4*
$ FILE=/etc/pulse/default.pa;mv $FILE-old $FILE
$ dpkg-reconfigure linux-sound-base # Select ALSA
$ reboot # This will RESTART your system!

Optionally, follow steps 5-6:
$ xdg-open https://trisquel.info/en/wiki/installing-oss4-trisquel-40#toc5

If the problem persist, use this:
$ echo [Desktop Entry]>>~/Desktop/spkmute.desktop
$ echo Type=Application>>~/Desktop/spkmute.desktop
$ echo Name=Speaker Mute>>~/Desktop/spkmute.desktop
$ echo Exec=ossmix jack.int-speaker.mute TOGGLE>>~/Desktop/spkmute.desktop
$ echo Icon=xfce-sound>>~/Desktop/spkmute.desktop
$ echo >>~/Desktop/spkmute.desktop
$ chmod +x ~/Desktop/spkmute.desktop

This will create a handy shortcut on your desktop with which you can toggle mute/unmute the internal laptop speakers. I also recommend you to put it on your panel, so you does not need to switch to desktop and double-click on it everytime you need it.

Also note, that these commands are originaly written for a shell script (made for my own purposes) so the code may look a bit unclean for a 'Terminal' use.

Hope this help.

Hey, I found this issue on my notebook with a Live CD, ran "$ alsamixer", and enabled the "auto-mute" option; this solved my problem. If you try it, let us know if it works for you.