* French yields hit lowest since mid-Jan
* Further falls expected if Macron wins TV debate
* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr
By John Geddie
LONDON, May 3 (Reuters) - A televised debate between France's presidential rivals on Wednesday could compound expectations for many investors that centrist Emmanuel Macron will topple far-right eurosceptic Marine Le Pen at a weekend run-off.
French government bond yields fell to their lowest since mid-January, while the gap to German bond yields -- a closely-watched gauge of political risk -- held near its lowest level since December, and the euro held near its highest in six months ahead of the evening debate.
Analysts said markets could rally further if Macron, who already holds a 20 point lead over Le Pen in the polls with just four days to go before the vote, wins Wednesday's encounter.
"We think European government bond markets could be tempted to start pricing a Macron victory in the last days of the week but this is likely to wait at least until the outcome of the debate tonight," Mizuho's head of euro rates strategy Peter Chatwell said.
Though Le Pen has a mountain to climb to catch Macron, the 2017 campaign for the Elysee has been packed with surprises, the exchanges between the two have become noticeably sharper and the 48-year-old National Front veteran has shown she is capable of catching him out with clever public relations manoeuvring.
Macron warned he would not pull his punches on Wednesday against a rival whose policies -- which include ditching the euro currency and impose sharp curbs on immigration -- he says are dangerous for France.
Macron finished only three points ahead of Le Pen in the first round on April 23, but he is widely expected now to pick the bulk of votes from the Socialists and the centre-right whose candidates were eliminated.
French 10-year bond yields fell 1 basis point on Wednesday to 0.738 percent, its lowest levels seen since mid-January.
The gap to German equivalents stood at around 43 basis points, near levels last seen in December.
Analysts are expecting further tightening of around 10 basis points if Macron triumphs in Sunday's vote. But if investors are convinced after tonight's debate, some of that may come in the last couple of trading days before the election, they said.
"If Le Pen fails to perform unambiguously better than her liberal rival (at the debate), this crossing of swords could already decide the battle in Macron's favour," DZ Bank strategist Daniel Lenz said.
Aside from the French election, investors will also be keeping an eye on a meeting of the U.S. Federal Reserve at which it may hint it is on track for a rate hike in June.
The central bank is scheduled to release its policy decision at 2 p.m. EDT (1800 GMT) at the conclusion of its two-day meeting. Fed Chair Janet Yellen is not due to hold a press conference.
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Additional reporting by Richard Balmforth