I've run this race for most of my grinding. Here are a couple of strategies:
1. Grab an R32, RX-7, RX-8, or something similar you can engine swap. The DeLorean and the Trans Am work for this, possibly even the Tundra. Many of these can win on easy difficulty with the stock engine, so don't swap just yet. Also the 1999 WRX road car can win as well.
I used the R32 a few times this way. Install RS tires, set ride height a tad above minimum, drop the stabiliser and damper setting one notch below stock, LSD to minimum on all, and upgrade everything that doesn't increase engine power to max. Leave the nitrous, hydraulic handbrake, and the steering adapter off. Set your downforce to max. You will need some body part from GT Auto for this. Also change the wheels and go with a rim diameter towards the middle with a wide stance. I use wide wheels but you may want to consider a narrow wheel to reduce hydroplaning. If a roll cage is available, use it. Use the standard license plate, pick a headlight color and a livery, and you're good. Back in Settings, set the gears to top out around 320. If you're running 4 wheel drive, start it out at 50:50. TCS should be set to 5, brake balance 0, and FM1. Even if you don't think you need TCS, anti lock brakes, and counter steer assist, use them. They reduce tire wear. I'd turn on ASM also. Leave Auto Drive off.
This car is going to drink fuel and destroy tires, period. You will be in the box every four laps, which works better with unpredictable weather.
Now look at your car's weight distribution. On a 50:50 car with four wheel drive, the front tires will wear faster. With a front-mid engine and rear wheel drive, tire wear will be fastest on the heavier end. Most of the game's four wheel drive vehicles have a front-mid mounted engine. I digress.
On the display settings, turn off the leader board. You don't need it.
The strategy here is basically put every four laps and drive the car like you stole it. The R32 is stupid fast in this setup but will slide some, the RX-7 takes those to the extreme. On dry pavement you may want to shift torque and braking to the rear wheels and reduce TCS to gain a bit more speed.
Once you start winning on easy, move to intermediate then hard. The RX-7 and the R32 will destroy the competition with engine swaps. The GT3RS Porsche seen in the movie could probably handle this race bone stock on any difficulty.
The second strategy is to use a tuned Group 3 car. Find out what that car's strength is and capitalize on it. The McLaren's strength is speed, so focus on that. The 911 RSR's strength is grip. I recommend starting on RH tires with these cars, or RM if you have the PP left after tuning for max power.
Last things before you ever start the race, go into settings and look at the torque line. You'll see on some cars this is almost flat, those are the ones you short shift. On higher revving cars like the RX-7, you'll need to shift closer to redline (around 9000 RPM on the RX-7).
Now for the track. There are two things you need to burn into your brain. #1, you are to run from Le Source to Les Combes and again from Stavelot to the chicane flat out, pedal to the metal, period. Two, in Les Combes, Malmedy, Ickx/Speaker's corner, and College, the racing lines are wrong.
So ... start out just after Le Source. Hit the gas hard, watch your entry to Eau Rouge (enter by turning hard left), and floor it through Radillion and down the Kemmel Straight. You will hop some curbs here. Move left and brake for Les Combes, exiting each of these two corners on the inside. The final right is Malmedy, exit that on the left at full throttle with two tires either at or on the curb. Fade right, then left again once Bruxelles (the hairpin) comes into view and take this corner carefully. Stay on the dry section of the track. Fade right as you hit the gas and aim for the inside curb on Ickx corner (the 90 degree left). At this point hit the gas hard. Accelerate all the way to Pouhon, the long, double apex left handed. This is gonna be an out-in-out-in-out corner and you should exit it at very close to top speed. Next is College, aim to exit the right hander on the inside, then cut hard and floor it to Paul Friere. This and Stavelot form a medium speed dual apex right hander. You should be able to punch it between the apexes and never let up til the final chicane, but first you gotta get through Blanchimont, the long sweeping left hand turn. Make sure you stay to the right except in the apexes, by this I mean keep two tires over the white line. Ignore the braking zones here.
On the final chicane, if you need to put, point the car parallel to the inside curb on the right hander and drive straight to the wall. If not, stay in first gear and feather the gas til you're on the pit straight. Brake a tad early and choose a line for Le Source, wide if no one is around, close to the wall if they are.
Should you find yourself out on slicks in the rain, obviously stay on the driest parts of the track. If you're on wets and it stops raining, do just the opposite. IM's are useless in this race, as you'll see when the AI puts every 3 laps for them.
On the weather radar, when you start getting dark blue at the edge, you have two laps til the rain hits. If it's real spotty, ignore it. If the dark blue, yellow, red, etc. is in a larger clump, go ahead and drop to FM1 and whatever brake balance handles best, put as much fuel and rubber as you can into distance, and be ready to pit 1-2 laps later. During the rain, tire wear shuts off, so focus on traction by enabling assists and maxing then (with the exception of Auto Drive, it sucks). Go to FM 6 to further reduce the tendency to break the drive wheels loose.
Use the track map to determine where the leaders are. You can also use it and the radar to run this race in a car that has no headlights. If you're using VR, you can still see the road without headlights. As in real life it's never totally dark out.
This should get you to first place in either a Group 3 car or a similar road car on any setting. Alternately you could run any Group 1 or Group X car detuned and smoke the entire field, but you won't learn to handle the heavier Group 3 and road cars that way.
Don't give up in the first few laps, especially if you're putting every 4 laps. You could easily be running 320+ km/h or 200+ mph top speeds, these will level the competition in the end.
Take note that the 911 RSR, the CLK-LM, and the 917k are all used in either CE's or license tests. If you did the Porsche specific time trial last summer you have a 917k already. All of them can win on any difficulty level but some will need tuning adjustments.
Lap times in the dry need to be 2:18 or better to win on hard, 2:21 or better on easy. If the track is wet, 3:00 is more realistic. Consider the track wet if the moisture meter is above the first line.
I hope this helps.