Marseille, who had been chasing a title since their 1993 Champions League triumph, ended their long wait by flooring Girondins Bordeaux 3-1 at the Stade de France.
NEWS:Marseille end trophy drought
The southerners, lying three points behind champions Bordeaux in the Ligue 1 race before Sunday's action, see no reason why they should stop there.
Marseille, who beat title contenders Olympique Lyon 2-1 in the league last week, believe they are strong enough to claim the championship for the ninth time, the first since 1992.
"This makes us hungry for more," Marseille president Jean-Claude Dassier told reporters.
"If we had lost (to Bordeaux), people would have said we were doomed but now we want the title. We will not be content with just the League Cup."
Midfielder Mathieu Valbuena, who scored a goal against Bordeaux, agreed that Marseille had the right to be ambitious.
"We can't stop there," he said. "The confidence we got from our wins against Lyon and Bordeaux will help us a lot."
Tough times followed Marseille's Champions League win, the club being stripped of their 1993 French title over a bribery scandal and demoted to the second division.
They recovered, however, and often came close to success, losing French Cup finals in 2006 and 2007 and the UEFA Cup finals of 1999 and 2004.
Now they want more, although coach Didier Deschamps, who captained the side who beat AC Milan 1-0 in the inaugural Champions League final in 1993 in Munich, sounded a cautious note.
"Let us enjoy this first," he said. "Then we will have a marathon with five matches in two weeks. We will see after those games if we can afford the luxury and the pleasure of fighting for the title."
FEATURE:Deschamps and Marseille happy to win cup nobody wanted
NEWS:Deschamps makes Marseille proud again
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