you can go into the logitech profiler and set your paddles to a key. so you can set the shift up and down paddles to the letter A and Z... and then ingame, set the shift up and down buttons to A and Z. or something like that... i cant remember.
in your /data/script/ folder you should have scripts for every car (which are executed automaticly when you leave the pits) and in you /docs/ folder you have a commands.txt which explains the basics of how to write these scripts (its also in the changelog)
unfortunately i cant remember where the list of available commands (like shift_up) to map to the buttons was
Go into LFS, go to the control screen and press the paddle buttons so it shows you what button number for each paddle. Then go into the BF1 script and enter /button 5 shift_up and /button 4 shift_down (change the numbers to whatever your paddles numbers are)
edit, after testing this it seems that it keeps the controls even after you change car. So you will have to assign gear shift button scripts for all cars.
Since by default each car has a script that runs either the paddle.lfs, road.lfs, or sequential.lfs script, you just have to edit those three scripts. For example here's my road.lfs (using a Momo):
// shift from shifter button 8 shift_up button 9 shift_down
// reassign paddles button 0 flash button 1 horn
And paddle.lfs:
// shift from paddles button 0 shift_down button 1 shift_up
// reassign shifter button 8 flash button 9 horn
Then you have to edit car scripts only if you don't want to use the default, like for example replacing "run sequential" with "run paddle" in MRT.lfs.
BTW, once these three scripts are set, you can also run them while driving. For example typing "// paddle" in the text box while driving the UF1 would instantly allow you to switch gears from the paddles rather than from the shifter.