Since the game is made on the Zdoom engine, it are very easy to activate these features.

Okey, you need to open Steam/Steamapps/Common/Supplice/Supplice.ipk3 file with SLADE editor (from DooM Community) or 7z/WinRAR or any other archiver.
Then open ZMAPINFO.TXT inside Supplice.ipk3.
find
*****************************************************************************
defaultmap
{
NoJump
NoCrouch
SmoothLighting
ClipMidTextures
EnterPic = "INTERPIC"
ExitPic = "INTERPIC"
}
*****************************************************************************
and erase
"nocrouch" and "nojump" strings, to become like this:
*****************************************************************************
defaultmap
{
SmoothLighting
ClipMidTextures
EnterPic = "INTERPIC"
ExitPic = "INTERPIC"
}
*****************************************************************************
Save ZMAPINFO.TXT

Then open
MENUDEF.TXT
and find this part:
*****************************************************************************
OptionMenu "SuppliceKeybinds"
{
Title "$SUMENU_KEYBINDS"
ScrollTop 2
StaticTextSwitchable "$CNTRLMNU_SWITCHTEXT1", "$CNTRLMNU_SWITCHTEXT2", "ControlMessage"

StaticText ""
StaticText "$SUCATG_MOVEMENT", 1
Control "$CNTRLMNU_FORWARD" , "+forward"
Control "$CNTRLMNU_BACK" , "+back"
Control "$CNTRLMNU_MOVELEFT" , "+moveleft"
Control "$CNTRLMNU_MOVERIGHT" , "+moveright"
Control "$CNTRLMNU_TURNLEFT" , "+left"
Control "$CNTRLMNU_TURNRIGHT" , "+right"
Control "$CNTRLMNU_RUN" , "+speed"
Control "$CNTRLMNU_TOGGLERUN" , "toggle cl_run"
Control "$CNTRLMNU_STRAFE" , "+strafe"
Control "$CNTRLMNU_USE" , "+use"
*****************************************************************************

Add these three strings:
Control "$CNTRLMNU_JUMP" , "+jump"
Control "$CNTRLMNU_CROUCH" , "+crouch"
Control "$CNTRLMNU_TOGGLECROUCH" , "crouch"

to become like this:
*****************************************************************************
OptionMenu "SuppliceKeybinds"
{
Title "$SUMENU_KEYBINDS"
ScrollTop 2
StaticTextSwitchable "$CNTRLMNU_SWITCHTEXT1", "$CNTRLMNU_SWITCHTEXT2", "ControlMessage"

StaticText ""
StaticText "$SUCATG_MOVEMENT", 1
Control "$CNTRLMNU_FORWARD" , "+forward"
Control "$CNTRLMNU_BACK" , "+back"
Control "$CNTRLMNU_MOVELEFT" , "+moveleft"
Control "$CNTRLMNU_MOVERIGHT" , "+moveright"
Control "$CNTRLMNU_TURNLEFT" , "+left"
Control "$CNTRLMNU_TURNRIGHT" , "+right"
Control "$CNTRLMNU_RUN" , "+speed"
Control "$CNTRLMNU_TOGGLERUN" , "toggle cl_run"
Control "$CNTRLMNU_STRAFE" , "+strafe"
Control "$CNTRLMNU_USE" , "+use"
Control "$CNTRLMNU_JUMP" , "+jump"
Control "$CNTRLMNU_CROUCH" , "+crouch"
Control "$CNTRLMNU_TOGGLECROUCH" , "crouch"
*****************************************************************************
Then Save MENUDEF.TXT and Save Supplice.ipk3.


Now in the key binding menu (inside the game) you will have a setting for jump and crouch buttons.

P.S. You should keep in mind that many of the levels and secrets were made by the developer with the inability to jump and crouch in mind, so activating these features may change or harm your gaming experience.