If memory serves,
It brought arcade style upgrades, simulation physics and livery editors together in one game.
That does depend entirely if you agree that the original Forza actually broke the mould in terms of simulation physics for a console, to be honest I would be more than happy to agree on the livery editor side of thing but the other two are very debatable.
Completely changed the way online racing is played with auction houses, tournaments and more.
More than happy to agree with this and its an area that the GT series needs to learn from.
Gave damage to 200+ cars in the original, 300+ in number 2 and now damage to 400+ cars.
The number of cars is totally irrelevent, fact of the matter is the TOCA series was doing damage on consoles long before Forza and arguable better.
It gives PC quality simulations to Console gamers as said by unbiased reviewers of racing sims.
Now that is working on the assumption that Forza (as in the original) is amore accurate sim that GT3 (which I would question) and also forgetting Enthusia, which released before FM. Not to mention Richard Burns Rally which released in 2004.
Brings all types of players together wether they be hardcore sim racers, creative painters or just casual car enthusiasts.
Most hardcore sim racers were quite dissapointed by the original Forza, hell most hardcore sim racers dismiss console titles (with the exception of RBR) full stop.
There is more but I can't be bothered to go on.
So, now list what GT has done that is new and/or revolutionary.
Oh and if I remember correctly Forza 1 was the first game that let you train the A.I yourself.