You can customize your controller setup in the input window pre-game.
To open this window:
On Mac: hold the options key while starting the game to open the setting dialog
On Windows: hold the options key while starting the game to open the setting dialog
On Linux: Add to the games launch options: -show-screen-selector
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Crash Drive's Layout for Xbox Controller

A=botton0
B=button1
X=button2
Y=button3
LB=button4
RB=button5
Back=button6
Start=button7
Middlebutton8

Axis 0 = Left Stick -right/left
Axis 1 = Left Stick -up/down
Axis 2 = Left Trigger
Axis 3 = Right Stick -left/right
Axis 4 = Right Stick -up/down
Axis 5 = Right Trigger
Axis 6 = D-Pad -left/right
Axis 7 = D-Pad -up/down
Axis 9 = Left Click
Axis 10 = Right Click

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1 possible configuration
that works for me except
no front and back flips or
Jump?, but everything else
seems to work, maybe I have
bad controller.

My configuration.
Button 3 = A = Horn
Button 2 = B = Speedboost
Button 1 = X = Handbrake
Button 0 = Y = Jump

Axis 5 = RT = Joystick/Vertical
Axis 7 = DP down= Handbrake
Axis 0 = LS left= Horizontal
Axis 4 = RS up= Vertical/Disabled

Note: D-pad down is Reverse ie: Handbrake?
Best Wishes from Ctheunicorn