Is time running out for France's President?

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French President Francois Hollande has suggested that he will not stand for re-election if the country's unemployment rate remains high, and with reforms slow to take off there are doubts he can achieve this and be re-elected in 2017.

Unemployment in the country hit 10.5 percent in September, according to Eurostat, and in a live television interview on Thursday Hollande discussed his failure to "invert the trend" of rising unemployment since taking office in 2012.

"Do you think I can say to the French people, 'I didn't manage it for five years, but I promise I'll do it in the next five?' It doesn't work like that," he said.

"If I don't manage it before the end of my term, do you think I will go before the French people in 2017? The French people would be unyielding and they would be right."

Speaking on channel TF1, the beleaguered leader also said he would impose no new taxes on people next year.

His comments came hours after polls showed that Hollande's approval ratings had hit a new low. In the worst score for a French president in modern-day polling, Hollande received a 12 percent approval rating in the monthly survey by polling company YouGov, down 3 percentage points from the previous month.

The falling ratings come amid a tide of pessimistic economic data for France.

On Friday, the Bank of France forecast that the French economy would grow by just 0.1 percent in the fourth quarter, after expanding by 0.2 percent in the third quarter from the second quarter.

The economy failed to grow at all in the first half of the year, data from French statistics bureau Insee showed. Meanwhile, recent flash Purchasing Managers' Index data showed that in October, manufacturing and services output slipped to 48.0 in France -- its lowest reading since February and a decline from 48.4 in September. A reading below 50 marks a contraction in private sector activity.

Read more: France should go 'at own pace': Finance minister

Amid this picture of slow growth, criticism of Hollande's apparent lack of policies to stimulate the economy has been forthcoming from the business world - a sector he alienated early on in his leadership when he proposed that companies pay a 75 percent tax on salaries over a million euros.

France's Constitutional Council scrapped the controversial tax but not before the damage was done to the president's relationship with the business industry, who accuse him of not doing enough to improve competitiveness, promote growth and reform the rigid labor market.

Read more: French lenders warn on 'difficult' economy

On Thursday, French lender Credit Agricole's Chief Executive told reporters in a conference call Thursday that "the absence of a clear vision and lack of coherence in economic policies is weighing on confidence and therefore investment and economic activity."

Threat from the Right

Hollande's attempts to appeal to voters have come too late, according to Henri Sterdyniak, an economist at the French Economic Observatory in Paris. He told CNBC that France had "to wait for more growth".

"Many people in France are very disappointed with (the government's) policy – some people want to vote for (the right-wing politician) Marine Le Pen and there is great disappointment with the capacity of policymakers to improve the French situation," he told CNBC Europe's "Squawk Box" on Friday.

Bob Janjuah, co-head of cross-asset allocation strategy at Nomura, agreed that some French voters would swing to the right and vote for Le Pen's and her Front National (NF) party in 2017. This had the potential to change the future of Europe, he warned.

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"France is the future of the euro zone, so if in 2017 it's Hollande versus Le Pen, she could win. And if that happens, I don't see how (German Chancellor Angela) Merkel and Marine Le Pen can do business together. I think at that point, that's (going to be) the main issue."

Janjuah predicted that the euro zone would post no economic growth over the next five years, adding: "more worringly, nominal GDP growth (across the euro area) could be lower than that."

He added that in France and in Europe generally there was a lack of investment and reform.

Not everyone was so pessimistic about Hollande's future, however. Reacting to the President's television address on Thursday, Olivier Mallet, chief financial officer of French steel pipe producer Vallourec, told CNBC that Hollande's comments were positive -- for the time being.

"Hollande and his new Prime Minister Manuel Valls are now fully recognising that in order for France to have growth, to create jobs and employment, the government has to create a favourable environment for firms and the private sector," he said.

"So…it's definitely positive news that Francois Hollande is now recognising that that is one of the key priorities."

- By CNBC's Holly Ellyatt, follow her on Twitter @HollyEllyatt. Follow us on Twitter: @CNBCWorld