Audi R8. Might cost an arm and a leg (unless you want to do the Le Mans 24 hours and win it there), but it's a dream to drive and unmodified, it can hold it's own with the best of them - even against the Minolta, Sauber-Mercedes, R92CP, R89C and, strangely, the Camaro LM Race Car. How the hell I got that draw was beyond me, but it's still winnable.
Just watch out for the 18 laps around Opera Paris Reverse. That track was NOT meant for LMPs at all and you'll just eat your tyres to the point where you'll have to two-stop (try around laps 6 and 12). Stupidly, I did a one-stop on lap 9 and was sliding around for the last three laps, and finished thrid (would have been fourth, but I beat the R89C by about 0.014 seconds).
Also, the competition will be fairly consistent - for me, the Sauber always finished second (bar Opera, where it won), and the Minolta always third. So unless you're like my brother and just punt the most-consistent bad guys off at the first corner (sending both of you into a spin) and then drive like hell to try and win, you'll also need to be good.
Oh yeah, and sometimes the AI thinks it doesn't need to stop at La Sarthe, so you'll need to drive hard, fast and perfectly to catch him on the final lap or two (or just let Arnage do the messy bit - three out of four times I've raced the series, the guy who skips his stop spins there).