* Industry output in October shows Q4 started badly
* Car industry continues to suffer
By Brian Love
PARIS, Dec 10 (Reuters) - France's central bank said on Monday it expected the euro zone's second-largest economy to contract in the fourth quarter of 2012, a state underlined by data showing tumbling car sales.
The Bank of France repeated a prediction that gross domestic product will drop 0.1 percent in the three month to the end of the year, compared with the third quarter.
A statistics office report separately showed that the troubles of France's car industry continue to take a heavy toll on overall activity, falling for a 12th straight month in October.
"These are quite dire numbers to be honest," said Joost Beaumont, an economist at ABN AMRO bank who, like the central bank and many other private-sector economists, expects GDP to drop in the fourth quarter.
Industrial output, which forecasters had expected to pick up marginally following a 2.7 percent plunge in October, dipped 0.7 percent in October versus September levels -- and a large part of that was due to a further fall of 4.7 percent in auto sector output.
There is little prospect of an rapid turnaround due to weak demand and overcapacity in the car sector both in France and internationally.
PSA Peugeot-Citroen, which plans to shed 10,000 jobs, is idling its Sochaux plant in eastern France for 19 days over the Christmas holiday period.
"In addition to the slowdown in growth resulting from the euro zone crisis, the weakness in the car industry should continue to be a drag in Q4 (the fourth quarter)," said HSBC bank economist Pierre-Emmanuel Ferraton.
The Bank of France stuck to its prediction of a small drop in fourth-quarter GDP despite news since it first made such a prediction that the French economy had fared better than many predicted in the third, July-September, quarter.
French GDP grew 0.2 percent in the third quarter, defying the Bank of France's prediction of a 0.1 percent drop, and also bucking the trend in the euro zone as a whole, which fell into recession with a second quarter of shrinkage in the third quarter.
Germany also secured 0.2 percent GDP growth in the third quarter but showed signs of weakness too in data on Monday.
The trade surplus in Europe's largest economy narrowed in October to its lowest level in over half a year as exports posted meagre growth in the face of weakening demand from the country's recession-hit European partners.
The Bank of France also noted that its industrial climate indicator dipped a further 1 point to 91 in a November survey, although a similar measure of sentiment in the services sector held steady at 91.
ABN AMRO's Beaumont said the October drop in industry output was all the more gloomy because economists had on average been expected a 0.3 percent rise, largely on the assumption that it had to improve after such a sharp drop in September.
But he and other economists said there were signs that the economy may have hit bottom.
"We expect France to resume modest positive growth in 1Q13