The actual answer is that Le Mans did not have a winner in 1923 nor, for that matter in 1924 or 1925 either, because these were not individual races but mere rounds of the Rudge-Whitworth Triennial Cup. The idea was a ploy pure and simple, cooked up by the Automobile Club de France and the French importer of Rudge-Whitworth bicycles, motorcycles and wheels to ensure teams kept coming back, which given the expense and risk of hosting the world’s first 24 hour race is probably fair enough.
Incidentally, Le Mans didn’t just introduce the world to 24 hour racing, in 1906 it hosted the world’s first Grand Prix too. International motor racing had been dominated by the Gordon Bennett Cup races since the turn of the century, which suited the French not at all because each participating nation could only enter a limited number of cars, and France had by far the largest car industry in Europe. So it suggested a new race with no such limit, put its money where its mouth was and called it a Grand Prix because the ‘prix’ for winning was absolutely enormous: 45,000 francs if you please. So if you ever wondered why everyone uses a French term every time the location of the next F1 race is discussed, now you know.
I digress. Unlike the Grand Prix which was held on a vast 64-mile road course to the east of the city, the first 24 hour race was held in its now traditional location, even if the track itself was very different. For a start a lap was 10.7 miles long, whereas today it is 8.5 miles. The difference is largely accounted for the fact that where the track turns right after the pits today and goes up through the Dunlop chicane and down through the Esses to Tertre Rouge, in 1923 it carried on into town, before turning sharp right by the Pontlieue bridge and heading back towards Tertre Rouge. This made the straight leading from the old White House corner (bypassed by the Porsche Curves in 1972) to Pontlieue almost as long as was the Mulsanne Straight from Tertre Rouge to Mulsanne before they broke it up with chicanes in 1990.