A new crisis of confidence gripped Europe's banking industry Thursday as its borrowing costs soared, lenders sought emergency funding, and some institutions reviewed exposure to French banks in particular.

Shares in Societe Generale , whose shares dropped 15 percent Wednesday, yo-yoed for most of the day, carrying other big French names in their wake this time. Attempts to reassure the market by the bank's boss and the governor of the Bank of France had little effect.

French banks have an unusually high exposure to some of the European countries whose debt levels are starting to look unmanageable.

They have big holdings of Italian government bonds and subsidiaries in Greece. Fears about France's own sovereign health and a reliance on strained short-term funding markets have made them a target in recent days.

But the loss of faith runs deeper and wider than the focus on SocGen and its fellows.

With banking rumors surfacing yesterday, it feels like the run-up to Lehman's collapse, where banks don't trust each other, said Commerzbank rate strategist Christoph Rieger.

The three-month euro-dollar cross-currency basis -- which reflects the premium for swapping euro Libor into dollar Libor -- widened to as much as 95 basis points, up around 40 bps since the start of August, though still well short of the 300 bps seen at the height of the financial crisis.

Emergency overnight borrowing from the European Central Bank surged, with banks taking over 4 billion euros of overnight funds from the ECB, the highest since mid-May.

The signals coming from Europe set off alarm bells in Asia. Banking sources told Reuters that one bank in the region had cut credit lines to major French lenders, while five others were reviewing trades and counterparty risk.

Investors saw the latest loss of confidence as a sign that few of the problems that brought bank lending screeching to a halt last time around have really gone away.

The market is already broken. It has never fully recovered anyway from 2008. Liquidity comes in fits and starts, and risk appetite in the banks is understandably very modest, said Stephen Snowden, fixed income manager at Aegon Asset Management.

SocGen shares were up 5.6 percent by 1440 GMT Thursday after falling as much as 9 percent, in volume nearly three times the average over the past 90 days.

The European banks index <.SX7P> was 3 percent higher, with BNP Paribas about flat, and Credit Agricole up 5.4 percent.

Earlier in the afternoon the cost of insuring SocGen debt against default had risen, with five-year credit default swaps 31 basis points wider at 365 basis points, Markit said.

Bank of France Governor Christian Noyer said Thursday that French banks were solid and that their solidity would not be affected by recent market turmoil.

Their capital levels, boosted by strong equity capital, are adequate, and their medium- to long-term financing programs are being carried out in perfectly satisfactory conditions, Noyer said in a statement.

WATCHDOG WARNS AGAINST Rumor-MONGERING

In an interview with Le Figaro newspaper, SocGen's Oudea said the bank had come under a series of attacks in the stock market. It had not experienced any losses in particular in the past few days, and its results to date were satisfying, he said.

To our clients, we have to tell them that these rumors are baseless and that they can have confidence in Societe Generale, Oudea told France Info radio. They should not listen to this stuff, which is totally baseless.

France's AMF financial watchdog issued a statement to warn against spreading unfounded rumors. SocGen has called on the AMF to investigate their source.

SocGen reaffirmed its ability to generate solid results in the future, based on its performance in July and early August. It added that it had successfully completed almost all of its 2011 financing plan.

It is quite likely in our view that funding will not become a serious issue for the large French banks, that anxieties subside and that the shares rebound, RBS analysts said.

But there is a non-trivial risk that confidence deteriorates further.

Investors have speculated SocGen may have to raise about 3 billion euros to reach new global capital standards if the euro zone crisis worsens.

The bank, still trying to rebuild its credibility after the Jerome Kerviel rogue-trader scandal in 2008 in which it lost 4.9 billion euros ($6.9 billion), also issued a profit warning last week.

One analyst said the aim of the attacks on SocGen was to force it into a capital increase.

SocGen, BNP Paribas and Credit Agricole together lost nearly 10 billion euros in market value Wednesday.

($1=.7099 Euro)

(Additional reporting by Matthieu Protard, Blaise Robinson, Alexandre Boksenbaum-Granier, Claire Watson and Leila Abboud in Paris; Rachel Armstrong and Saeed Azhar in Singapore and Natalie Harrison, Steve Slater, Sinead Cruise and Alex Chambers in London; Editing by Geert De Clercq, Andrew Callus and Will Waterman)