PARIS (Reuters) - The French economy is set to grow slightly more strongly than expected in the third quarter of 2024, as industrial activity gained pace in September and hosting the Olympic Games in Paris boosted the service sector in August, the central bank said on Tuesday.

But the country's political crisis and uncertainty tied to the new government's policies for the economy and budget, as well as international conflicts, are clouding the economic outlook, the bank said in its monthly business survey.

After weeks of struggling to find a new prime minister, President Emmanuel Macron named conservative political veteran Michel Barnier to the post last month, who now faces the difficult task of getting the 2025 budget approved and bringing down the deficit in the deeply divided post-election parliament.

The euro zone's second-biggest economy is on course for underlying growth of 0.2% in the third quarter, up from a previous estimate last month of 0.1-0.2% growth, the bank said.

The Olympics could add another quarter percentage point of growth as the Games increased activity in hospitality, event management and security, particularly in the Paris region.

That effect however faded in September, with activity slowing down in leisure, car rentals, temporary employment and hospitality, the bank added.

Last month France's national statistics agency INSEE forecast the economy would see 0.4% growth in the third quarter, but would then reverse into a 0.1% contraction in the fourth quarter as the Olympics boost fades.

The central bank's monthly survey of 8,500 businesses found that activity would remain sustained in industry in October, but subdued in some services sectors such as temporary employment and leisure.

Meanwhile, the construction sector remained weak in September with negative sentiment on order books.

Recruitment difficulties declined only slightly, with 35% of businesses reporting challenges in September, against 36% in August.

(Reporting by Dominique Vidalon; Editing by Alexandra Hudson)