I can almost guarantee you won't see much close racing and even less side-by-side racing. However, I still greatly enjoyed the racing. There was always drama (I personally once blew a one-minute lead with two crashes in the second half of such a Group C race) and if you have a large grid, such races always create a sense of occasion too.
It would be a one-time thing, kinda like these touring cars. But I like that sense of occasion, the handful of day-night-day races we've done had that feeling and I really enjoyed it.
But......I might have thought up a way to make it a bit more exciting and possibly add to the sense of occasion. It's not really a new idea, but a slightly different way of applying it.
The "theme", if you will (all details are for example only) would be a 12 lap race (with time change) and two "artificial full course cautions". In practice we would actually do three back-to-back-to-back races, the few minutes of break between the races would the be "caution periods". This caution period is mearly figurative to add to the "theme" of a Le Mans race. But what it would do is bunch the field back up and give everyone more close quarters racing.
The first race could be, for example, 2 laps, the second race 4 laps, and the third race 6 laps. Or 2, 5 and 5, or 2, 6 and 4. The second and third race could either start with "results from previous race" which would put us right back in the order we were, basically like restarting after a "caution".

Or, we could do reverse grid if we wanted to really make things interesting. 💡
I could see scoring it a couple different ways, shortest overall elapsed time or average finish between the three races. To do elapsed time I would add up each drivers elapsed times from the three races, lowest time wins. To do average finish I'd just take the average of everyone's finishing position, best overall average wins. Either way, the idea is that it's one big event, not three smaller events.
Calling the break between the races a "caution" is just to illustrate the thought that it's really one big race. Or we could call them "driver changes".

But since we'd bunch the field up a couple times it should keep things from getting spread out and boring. Doing reverse grid would be a way to help balance between the slow and the fast drivers and it would give everyone a chance to run up front. Also, we could have a smoke/pee break between the races if necessary! lol If we really wanted to balance the field we could have the top two drivers after each race limit their engine 5 or 10pp , kind of like a "penalty ballast". I could just change the restriction to 570pp real quick, have those two enter, then change it back to 575 for everyone else to join. By the third race, the longest race of the three, we'd have a fairly well balanced field. 💡
Just brain-storming here, but that seems like it could work well. People could race just one or two of the races if that's all their schedule allows. It satisfies the urge for competition knowing you have to do well over all three races, and without the need for a big points system. It keeps the race from becoming "glorified hot-lapping". If you make a mistake or get caught in a crash early your evening won't be wasted. Lots of positives. 👍