Make tridactyl layout-independent (Since 1.23.1 or pre6655)

Set keyboardlayoutbase to the desired layout and then set keyboardlayoutforce to true.

After that tridactyl will treat all shortcuts as if you use the selected layout, regardless of the layout selected in OS.
Examples:

qwerty

set keyboardlayoutbase qwerty
set keyboardlayoutforce true

azerty

set keyboardlayoutbase azerty
set keyboardlayoutforce true

german

set keyboardlayoutbase german
set keyboardlayoutforce true

dvorak

set keyboardlayoutbase dvorak
set keyboardlayoutforce true

uk

set keyboardlayoutbase uk
set keyboardlayoutforce true

bepo (but you probably want azerty?)

set keyboardlayoutbase bepo
set keyboardlayoutforce true

ca

set keyboardlayoutbase ca
set keyboardlayoutforce true

For further customization you can set separate mappings with keyboardlayoutoverrides or open an issue to include your layout. In the latter case, provide the output of this tool.

Before 1.23.1 (legacy, not recommended)

Using Tridactyl with a Cyrillic keyboard layout

The following makes the left column of key presses appear to Tridactyl as if they were the right column of keys. Credit goes to @dydascal. Add it to your tridactylrc if you have the native messenger installed.

keymap , ?
keymap . /
keymap / |
keymap а f
keymap А F
keymap б ,
keymap Б <
keymap в d
keymap В D
keymap г u
keymap Г U
keymap д l
keymap Д L
keymap е t
keymap Е T
keymap є '
keymap Є “
keymap ж ;
keymap Ж :
keymap з p
keymap З P
keymap и b
keymap И B
keymap і s
keymap І S
keymap ї ]
keymap Ї }
keymap й q
keymap Й Q
keymap к r
keymap К R
keymap л k
keymap Л K
keymap м v
keymap М V
keymap н y
keymap Н Y
keymap о j
keymap О J
keymap п g
keymap П G
keymap р h
keymap Р H
keymap с c
keymap С C
keymap т n
keymap Т N
keymap у e
keymap У E
keymap ф a
keymap Ф A
keymap х [
keymap Х {
keymap ц w
keymap Ц W
keymap ч x
keymap Ч X
keymap ш i
keymap Ш I
keymap щ o
keymap Щ O
keymap ъ ]
keymap Ъ }
keymap ы s
keymap Ы S
keymap ь m
keymap Ь M
keymap э '
keymap Э “
keymap ю .
keymap Ю >
keymap я z
keymap Я Z
set keytranslatemodes.ignoremaps true
set keytranslatemodes.hintmaps true

Using Tridactyl with a bépo keyboard layout / Utiliser Tridactyl avec une disposition de clavier bépo

keymap b a
keymap é z
keymap p e
keymap o r
keymap è t
keymap ^ y
keymap v u
keymap d i
keymap l o
keymap j p
keymap a q
keymap u s
keymap i d
keymap e f
keymap c h
keymap t j
keymap , g
keymap s k
keymap r l
keymap n m
keymap ç %
keymap à w
keymap y x
keymap x c
keymap . v 
keymap k b
keymap ' n
keymap q ,
keymap g ;
keymap h :
keymap f !

Using Tridactyl with an Arabic keyboard layout / استخدام Tridactyl بكيبورد عربية

keymap ش a
keymap ِ A
keymap ئ z
keymap ~ Z
keymap ث e
keymap ُ E
keymap ق r
keymap ٌ R
keymap ف t
keymap لإ T
keymap غ y
keymap إ Y
keymap ع u
keymap ` U
keymap ه i
keymap ÷ I
keymap خ o
keymap × O
keymap ح p
keymap ؛ P
keymap ض q
keymap َ Q
keymap س s
keymap ٍ S
keymap ي d
keymap [ D
keymap ب f
keymap ] F
keymap ا h
keymap أ H
keymap ت j
keymap ـ J
keymap ل g
keymap لأ G
keymap ن k
keymap ، K
keymap م l
keymap / L
keymap ة m
keymap ' M
keymap % %
keymap % %
keymap ص w
keymap ً W
keymap ء x
keymap ْ X
keymap ؤ c
keymap { C
keymap ر v 
keymap } v 
keymap لا b
keymap لآ B
keymap ى n
keymap آ N
keymap و ,
keymap ك ;
keymap ! !
keymap / /