UPDATE 1-Bank of France raises growth forecast slightly
* Business sentiment seen rising in both industry and services
Improving outlook offers relief as government drafts budget
(Adds details on survey)
PARIS, Sept 9 (Reuters) - France should post economic growth of 0.2 percent in the third quarter, the Bank of France said on Monday, revising its forecast up slightly from a first estimate of 0.1 percent.
Europe's second-biggest economy emerged from recession with faster-than-expected growth of 0.5 percent in the second quarter, but many economists have questioned it can keep that pace up for the rest of the year.
The Bank of France said its monthly business climate survey in August showed sentiment in the industrial sector rose to 97 from 95 in July, bringing the index to its strongest level since September 2011 and just shy of its long-term average of 100.
In the services sector, confidence also rose in August, reaching 93 on the central bank's index from 91 in July.
Executives told the Bank of France they expected activity to accelerate in September, with order books no longer shrinking in industry and staff levels on the rise in the services sector, a big employer.
Consumer confidence and import figures on Friday also signalled that demand in the 2 trillion euro economy is gathering momentum, although from low levels.
The improving economic outlook will provide some relief to the unpopular government of President Francois Hollande as it drafts a tough 2014 budget aimed at cutting the deficit to an EU limit of 3 percent of output.
The Socialist government's new growth new forecast will be closely scrutinised when it unveils the budget on Sept. 25.
The Organisation for Economic Cooperation and Development forecast last week that the economy would grow 0.3 percent this year, lifting its estimate from a contraction of -0.3 percent previously.
(Reporting by Leigh Thomas; Editing by Brian Love and Patrick Graham)