PARIS--The Bank of France cut its French growth forecasts Friday and said the country's government will fail to meet its deficit reduction pledge next year without extra spending cuts.

The central bank's gloomier forecasts will weigh on the upcoming presidential elections as candidates spar over how to cut spending and taxes without hurting the slow economic recovery and weak job market.

The Socialist government of Francois Hollande says it is on track to bring the deficit below the European limit of 3%. But the center-right candidate Francois Fillon--who polls show is favorite to win the election in May--is pledging deep tax cuts and expects the deficit to rise above 4% next year.

The Bank of France cut its growth forecast for this year by 0.1 percentage point and by 0.2 percentage points in 2017 and 2018. It now expects 1.3% gross domestic product expansion this year and next and a slight acceleration to 1.4% in 2018.

The deficit will decline to only 3.1% of GDP in 2017 from 3.3% in 2016 as spending growth accelerates due to new measures in education, security and employment training, the Bank of France said.

The central bank's governor Francois Villeroy de Galhau said the rate of deficit reduction is too slow compared with France's European neighbors. Another 4 billion euros ($4.25 billion) of savings measures would be necessary to meet the 3% target next year, he said.

"The 3% is important because it is the condition of our credibility in Europe," Mr. Villeroy de Galhau said on radio station BFM Business. "For us to be listened to, we need to be believed."

-Write to William Horobin at william.horobin@wsj.com