Boy, you going way back, this mod was out before I got the US v1.2 Flatout 1 that got me hook on Flatout.
I did some Googling and found this thread at NoGripRacing Forums > PC Racing > Other PC racing titlesRealistic handling mod
The guy Midi posted link to the mod you are looking for, ya links don't work any more, But you could try and PM Midi and see if he still has the mod or start a thread asking for the mod.
I also notice Bugbear Devs, fredizzimo and spikey, made posts\threads in The Flatout section. If want to get a some tidbits on Flatout 1, might give these threads here a read: NoGripRacing Forums > PC Racing > FlatOut series
It would seem we owe online racing with Flatout 1 back in 2004-2005 to Fred. Thanks Fred. http://www.nogripracing.com/forum/showthread.php?t=2230
I believe Fred still working at Bugbear. At least he was posting in the Ridge Racer Unbounded Steam forum back in 2012.