More than 8,000 away supporters and an enthusiastic home crowd helped to create a fine atmosphere at the Grand Stade Lille Metropole.
However, the action on the pitch was competitive but produced few clear-cut chances, with Aiden McGeady going closest to breaking the deadlock.
The Merseyside club had already beaten Wolfsburg and picked up a point at Kuban Krasnodar in Group H, so remain unbeaten.
So too do Lille, who drew 1-1 with the same two opponents and have been struggling for goals in the French top flight this season, scoring just eight times in 10 fixtures.
On-loan Liverpool forward Divock Origi showed plenty of pace and endeavour, but Tim Howard was seldom called into action.
Lille were still without on-loan Manchester City playmaker Marcos Lopes through injury but brought in Senegal duo Idrissa Gueye and Pape Ndiaye Souare after losing at home to Guingamp in Ligue 1 on Saturday.
Everton made six changes from their weekend win over Aston Villa, with Tony Hibbert, Sylvain Distin, McGeady, Steven Pienaar, Muhamed Besic and Samuel Eto'o called up.
A tight first 15 minutes ended with Besic being harshly booked for a high tackle after he clearly played the ball.
Eto'o had a chance to put Everton ahead but got the ball caught up in his feet, while Gueye grazed the post with a fierce shot from the edge of the area at the other end.
Howard comfortably dealt with a long-range Ronny Rodelin effort and Florent Balmont tried another speculative strike from long distance but it remained goalless at the break.
Lille had a penalty appeal turned down in the 55th minute after a cross struck Leighton Baines, with Franck Beria and Pienaar both booked as a dispute over the incident escalated.
Roberto Martinez introduced Romelu Lukaku for Pienaar and he made an immediate impact to set up McGeady, but Vincent Enyeama did well to save with his body.
Both teams continued to push forward at every opportunity but could not manage to conjure up a winning goal.
The two meet again on October 23 at Goodison Park.
