I haven't played this game since when it was new but I am pretty sure you don't have to do anything special for this...

...anyway, take the first track for example. I can't make the jumps (for instance, where the repair stations are or when you come out of the first 1/4 of the track to jump across the main drag) because my car does not get enough hang time and height (basically for that repair part I crash into the side of that platform). I think I have the car set to how I used to race (100 speed, accel, grip, 0 handling and brake) and I'm pretty sure there was no trick to this so I was wondering if the game speed/physics might be slightly off with more modern machines?

I'm new to this game but I've noticed this jump (on the repair platform) may be tricky, or even impossible on Easy mode, or Normal even, because the difficulty setting also limits your max speed. Cars will always be faster on Hard, however you set them. As far as I know, if you play on Hard, this jump should be possible even with a slower car (if you take full advantage of the slope). In any case, you can still use the repair station when you come back the other way, on your right.

Yes, I played this game a lot back in the 90s and the jump wasn't possible in easy mode, either. The car physics work exactly how I remember them.

The jump in Beltane is a tricky one.

It doesn't work in Easy at all, and you can only get it with much luck on Medium - of course if you have no damage at all.
In Hard, you can get it most of the times, but not if your front is damaged too much (local damage).

However, to repair in Easy or Medium, there's a small passage before the ceiling on the right of the street if you drive in the direction start -> tunneled hill (e.g. the other way round compared to the jump). It steals several seconds for you, but it's the only way to get up there.