Given that the two current Formula cars (XR and V8) are based somewhat loosely on real cars (XR on Formula Renault 2.0L and V8 on F3000 cars), Formula [Renault] 3.5L would be a bad choice to emulate, as they put out 425hp, pretty close to the FO8's power output.
The upcoming GP3 series would make a bit more sense (though maybe not enough) as they have 2.0L turbocharged I4s putting out 280hp. That's a bit closer to the FOX than it is to the FO8 in my opinion.
The next more powerful Formula car that I know of are the Formula 2 cars that have 1.8L turbocharged I4s puttng out 400hp.
Of course it doesn't have to be based on something in real life, but since all other cars are to some degree it makes it a bit tricky to have a 300-350hp Formula car, since none exist to my knowledge. As a whole I like this idea though, a meaner FOX would be fun.