Halep, who was beaten by Lucic-Baroni at last year's US Open, had to play catch-up for a majority of the first set after going 3-1 done before recovering to 3-3. She then found herself trailing 5-3 before rallying back to level matters at 5-5.
However, it was at this point that Lucic-Baroni began to pull away and she ended up dominating the remainder of the match.
Halep, who arrived at Roland Garros hoping to avenge her loss to Maria Sharapova in last year's final, admitted that Lucic-Baroni had outplayed her.
"She played well," Halep said after the match. "I couldn't play my best today, but she started to hit the ball very strong at the beginning of the match, and she was better than me today. I just have to go forward."