Nancy had Benjamin Moukandjo Bile sent off for a second bookable offence in the 80th minute.
A capacity 50,000-crowd packed the new Grand Stade Lille Metropole, the fourth home in the club's 68-year history, but eventually left frustrated.
Lille, the 2011 double winners and third in Ligue 1 last season, had almost all the possession in the first half but made little of it.
Nancy went ahead from their first real attack when Bakar curled a 25-metre shot past keeper Mickael Landreau after 33 minutes.
Ivory Coast international Kalou, who joined in the close season after helping Chelsea to their Champions League final triumph in May, headed the equaliser from Marvin Martin's cross.
That made up for an earlier miss when Kalou failed to hit the target after being put clean through on goal.
The result left both teams with four points from their opening two games.