Merci à tous ceux qui ont répondu, j'ai finalement trouvé 🙂
Avec ma carte intel, il faut utiliser l'option "ZaphodHeads" :
https://www.x.org/releases/X11R7.7/doc/man/man4/intel.4.xhtml
Les parties concernées du xorg.conf sont :
Section "ServerLayout"
Identifier "Layout0"
Screen 0 "Screen0" 0 0
Screen 1 "Screen1" RightOf "Screen0"
InputDevice "Keyboard0" "CoreKeyboard"
InputDevice "Mouse0" "CorePointer"
Option "Xinerama" "off"
EndSection
Section "Monitor"
Identifier "VGA1"
VendorName "Unknown"
ModelName "SONY TV"
EndSection
Section "Monitor"
Identifier "HDMI1"
VendorName "Unknown"
ModelName "LG W2600"
Option "Primary" "true"
EndSection
Section "Device"
Identifier "Card0"
Driver "intel"
BusID "PCI:0:2:0"
Screen 0
Option "ZaphodHeads" "HDMI1"
EndSection
Section "Device"
Identifier "Card1"
Driver "intel"
BusID "PCI:0:2:0"
Screen 1
Option "ZaphodHeads" "VGA1"
EndSection
Section "Screen"
Identifier "Screen1"
Device "Card1"
Monitor "VGA1"
DefaultDepth 24
SubSection "Display"
Viewport 0 0
Depth 24
EndSubSection
EndSection
Section "Screen"
Identifier "Screen0"
Device "Card0"
Monitor "HDMI1"
DefaultDepth 24
SubSection "Display"
Viewport 0 0
Depth 24
EndSubSection
EndSection