The French marque's A480-Gibson has been given an extra 7kW, or a little over 9bhp, bringing its power output to 427kW (573bhp).
It marks the second increase given to the Alpine ahead of this weekend's FIA World Endurance Championship centerpiece race, after it was given a power boost ahead of last weekend's test day.
However, the A480 will still be producing less power than it did at Le Mans last year, when the Alpine ran with 450kW (603bhp).
In the opening round of the WEC, where Alpine trio Nicolas Lapierre, Matthieu Vaxiviere and Andre Negrao scored victory, the car ran with 430kW (577bhp).
In addition to the extra power, Alpine has also been given an extra 11 megajoules of energy to use per stint, something that should help the team to hit its target of 12-lap stints around the Circuit de la Sarthe more consistently.
Both the Toyota GR010 Hybrid and Glickenhaus 007 LMH did not see any changes in the latest BoP.
Toyota team boss Rob Leupen suggested earlier on Wednesday that Alpine had not been showing its full hand during Wednesday's free practice and first qualifying session, when Lapierre was fourth-fastest in the five-car Hypercar class, 2.4 seconds slower than the pace-setting GR010.
"I think they'll be a bit closer [in Hyperpole] than they are now," Leupen told Motorsport.com, referring to Alpine's pace on Wednesday.
