Speaking to SPOnG, Turn 10's creative director Dan Greenawalt had this to say:

I knew that I wanted this car-collecting element to be implemented into the game. What game, especially back in 2002, had inspired collecting more than Pokémon?

It did collecting using a rarity system - through different coloured versions - with a sense that everything felt very natural. And actually, there’s a really natural sense of rarity in cars. So in Forza 1, the cars had a rarity meter, and you had to pick your region - much like choosing Pokémon Sapphire or Ruby - and that made certain cars more or less rare in the game. That was directly inspired by Pokémon.

So, yet more proof of Nintendo's strong creative influence in the industry...Earlier on this week, Wipeout's creators noted Mario Kart, not F-Zero, as being a major inspiration behind that series.