The race still had more than 23½ hours to go, but there was no call to stop it on Saturday after the first driver fatality in 16 years.
Simonsen's partner Carina, the mother to their daughter born last year, made sure of that.
It was her "specific request" that Simonsen's team, Aston Martin Racing, continue the world's most renowned endurance race in honor of the Dane.
Just 10 minutes into the race, Simonsen spun and skidded into the barrier at the Tertre Rouge corner where cars typically reach speeds of up to 105 mph. The 34-year-old Simonsen was taken to a hospital, where he died of his injuries, race organizers said.
The violence of the impact showed as a tire from Simonsen's car rolled on the track while a door hung wide open. The race was held up for nearly an hour to repair the guard rail.
"Tragically, and despite the best efforts of the emergency services in attendance, Allan's injuries proved fatal," Aston Martin said in a statement.
Simonsen's death marked the first driver fatality since 1997 when Sebastien Enjolras was killed in pre-qualifying. The last driver fatality during the race was Jo Gartner in 1986.
Simonsen was participating for the seventh time at the endurance race, which is won by the team that completes the most laps in 24 hours with up to three drivers alternating. He finished second in the GT2 class at Le Mans three years ago. He clocked the fastest time in qualifying on Thursday in the GTE-Am class.
Jean Todt, the FIA president, and Pierre Fillon, president of the Automobile Club de l'Ouest which organizes the race, paid tribute to Simonsen.
"Allan was an extremely talented and experienced sportscar driver who had raced in every corner of the world and was highly respected by his peers and his team," they said in a joint statement. "For many in endurance racing, Allan was above all a good friend who displayed his passion for racing on and off the track. His loss will be felt by the FIA, the ACO and the greater motorsport family."
Simonsen and Danish co-drivers Kristian Poulsen and Christoffer Nygaard were leading the GTE-Am class in the world endurance championship after topping their category at Silverstone in April and finishing second in Spa-Francorchamps last month.
"Aston Martin Racing will not make any further comment until the precise circumstances of the accident have been determined," Simonsen's team said.
Toyota Racing team president Yoshiaki Kinoshita expressed his condolences, along with drivers from around the world.
Formula One driver Jenson Button tweeted: "Allan Simonsen RIP. Such a tragic loss. A true fighter & a true racer. Safety is something we need 2 improve on in Motorsport."
IndyCar Series leader Helio Castroneves tweeted: "Very sad to know about the fatal accident of Allan Simonsen on Le Mans today. Praying for him and (his) family."
Another IndyCar driver Tony Kanaan tweeted: "Such a tragic news on the passing of AllanSimonsen. Sad day in motorsports again. Thoughts and prayers are with his family."