The warning from Manfred Weber, Chair of Parliament's EPP group, comes after his Socialist counterpart declared an end to the traditional agreement between the two groups.
Over the years this has seen close cooperation on legislative files. The two groups have also shared the Parliament presidency, with the Socialists taking the top job for the first half of a parliamentary mandate and the EPP the remainder.
But, on Tuesday, Gianni Pittella, who leads the Socialist group, said this arrangement would now cease.
Speaking at a news conference in Strasbourg, the Italian said, "The grand coalition is over and I cannot see it being reinstated.
"To be honest, I was never keen on the phrase 'grand coalition' because it was more of a case of legislative cooperation between the two sides."
On his bid for the Parliament presidency, Pittella said, "I am standing not because I want a badge on my lapel or because I am desperate to be the President.
"But I will continue to stand right through to the final round of voting. I do not know if I will win and my victory is far from certain but I hope this will open a new chapter in the history of the Parliament."
However, Pittella's decision to call a halt to cooperation between his group and the EPP was condemned by Weber.
The German MEP, who was also speaking in Strasbourg on Tuesday, said, "I am very surprised by this because we have, traditionally, enjoyed good cooperation with the Socialist group.
"This cooperation has always been very positive and has included working on thousands of legislative files.
"I hope this long standing agreement and partnership can continue because, if it does not, what it could lead to is people like Le Pen et al being able to win votes in Parliament on decisive issues.
"The worst case scenario is that Le Pen and Farage and people of that ilk will in future become the kingmakers in this institution."