(Reuters) -- European stocks rose to a five-week closing high on Monday, after French president Nicolas Sarkozy and German chancellor Angela Merkel agreed on a range of measures to help resolve the Eurozone debt crisis.

Banks rose sharply, with the STOXX Europe 600 Banking Index .SX7P up 2.5 percent, though it is down nearly 30 percent in 2011 with many banks having suffered heavy writedowns on exposure to euro zone sovereign debt. France's BNP Paribas (BNPP.PA) rose 4.9 percent and is up 33 percent from a low of two weeks ago.

The FTSEurofirst 300 .FTEU3 index of top European shares rose 0.8 percent to 993.27 points, the highest close since Oct. 31 and following last week's 8.5 percent jump, on growing optimism that action will be taken to stem the crisis.

There's some reassurance in the statement. They're talking about treaty change by March. They're moving in the right direction. And we've seen some short covering, said Ian King head of international equities at Legal & General, which has 356 billion pounds ($559 billion) under management.

The leaders of France and Germany agreed a master plan for imposing budget discipline across the Eurozone, saying the EU treaty will need to be changed in the search for a sweeping solution to its debt crisis.

Sarkozy said the Franco-German agreement was very complete and will be written up in a letter and presented to European Council President Herman Van Rompuy on Wednesday, ahead of a key EU summit on Friday.

Other developments in Eurozone countries helped to buoy sentiment. Italy's FTSE MIB .FTMIBgained 2.9 percent after the Italian government unveiled a fresh package of 30 billion euros of austerity measures. This eased tensions surrounding the country's finances, with Italian 10-year bond yields dropping towards six percent.

Financial services group KBC (KBC.BR) soared 12.9 percent as Belgium's one-and-a-half year search for a new government drew to a close, sharply drawing down yields on Belgian government bonds. Belgium's benchmark BEL20 .BFX rose 1.9 percent.

But strategists warned that the recent rally for equities may soon peter out.

Markets have had a good bounce, so there's scope for disappointment, said King, adding that cyclical sectors such as construction, materials, autos and chemicals would be especially vulnerable, given the view that the region was headed for a recession.

Despite Monday's gains on the market, The Euro STOXX 50 volatility index .V2TX -- Europe's yardstick of investor sentiment known as the VSTOXX -- rose 0.8 percent, signaling investors' hesitation about piling into risky assets before Friday's summit.