Fears of a strong performance of the anti-EU far-right and radical left candidates had weighed on equities and currencies in the European Union's emerging markets.
Warsaw led a rebound of stocks, with its blue-chip index rising 1.3 percent by 0740 GMT. The zloty gained 0.4 percent, the Czech crown 0.3 percent and the forint 0.2 percent. Volatility gauges for the  region fell sharply.
The Polish and Hungarian currencies bounced back from multi-week lows. One Budapest-based dealer said there was unusually brisk trade in the forint's dollar cross after a jump by the euro to a five-month high against the dollar.
"The French election outcome, with all the earlier fears, matched expectations. One risk is removed now," one dealer said.
The leu missed the rally, trading flat at 4.5355 to the euro. The government is expected to submit a bill to parliament on Monday setting out further increases in public sector wages. The Romanian net average wage jumped 14.7 percent in annual terms in February.
Romania auctions two-year government bonds on Monday.
The Czech crown reversed an earlier slide on Monday. It failed to make the gains many investors had bet on before the central bank removed a cap on the crown's value at 27 to the euro on April 6.
The currency crown could remain volatile for months, Czech central bank Governor Jiri Rusnok said on Friday. The bank will let the market find a rate for the crown it considers proper, he said.
In Hungary, anti-government protests have caused jitters in markets in the past three weeks, after the government passed legislation targeting a university founded by billionaire George Soros
The Hungarian central bank is expected to retain its loose monetary policy at its meeting on Tuesday.
Hungarian government bond yields dropped 2 to 3 basis points in early trade, in contrast with a slight rise in yields in Poland tracking German Bunds.
"The yield drop may have been triggered by the forint's gains," one Budapest-based trader said.