Having started the season emphatically with two wins and nine goals, Lyon has picked up only one point in two games after losing 1-0 at Montpellier on Tuesday.
Netherlands forward Memphis Depay put Lyon ahead in the 32nd minute, confidently beating goalkeeper Benoit Costil for his fourth goal in four games this season.
But Lyon midfielder Thiago Mendes was sent off in the 62nd for a second yellow card and former Lyon forward Jimmy Briand equalized five minutes later.
Lyon is in fourth place and Bordeaux is ninth.
Angers took advantage to beat last-place Dijon 2-0 and leapfrog Lyon into third spot with nine points. Also Saturday, midfielder Abdoulaye Toure scored an 85th-minute winner as Nantes beat Montpellier 1-0 to go fifth with seven points, trailing Lyon on goal difference.
In other matches, sixth-place Toulouse won 2-0 at home to lowly Amiens and Nimes beat Brest 3-0.
On Sunday Rennes needs only to draw at home to Nice to overtake Paris Saint-Germain in top spot, and it’s Marseille vs. Saint-Etienne as two storied French teams meet.
PSG won 2-0 at Metz on Friday.