The euro is falling at the start of the week.
Former French prime minister Alain Juppe ruled out standing in the country's presidential elections, which investors saw as increasing the likelihood of a victory by anti-EU leader Marine Le Pen.
A poll on Friday had suggested that if Juppe replaced the scandal-hit Francois Fillon as the centre-right candidate, he would win the election's first round, with centrist candidate Emmanuel Macron coming second - a scenario that would knock Le Pen out of the race.
But with Fillon in contention, polls suggest Le Pen would come either first or second in the first round and would then face Macron in the final run-off. Although polling suggests the far-right leader would lose to Macron or even to Fillon, investors are mindful of surprise vote outcomes.
The news sent the euro 0.4% lower to $1.0577, down from a two-week high it touched earlier in the day.
French government bond yields edged up on the news, with the gap between 10-year French yields and their German equivalents widening to almost 64 basis points, off a one-month low hit on Friday just below 58 bps.
"Everybody fears (a Le Pen victory) could have a tremendous impact on the common currency, as she's indicated that she wishes to exit from the euro," said Commerzbank currency strategist Esther Reichelt, in Frankfurt.
A source told Reuters on Monday that allies of former French president Nicolas Sarkozy are asking fellow Republican Fillon to find a replacement candidate.
News earlier in the day of North Korea firing four ballistic missiles, saw investors buy into the yen, with the dollar 0.3 percent lower at 113.80 yen, down from Friday's two-week high of 114.75.
After retreating to a one-week low in early European trading, the dollar recovered against a basket of major currencies, up 0.1 percent at 101.60 by 1235 GMT.
Federal Reserve Chair Janet Yellen on Friday said the U.S. central bank was set to lift its benchmark interest rate this month, provided jobs and inflation data hold up, which markets saw as cementing a hike at the bank's next meeting.
Fed funds futures pricing shows traders see around an 80 percent chance of a rate increase this month, up from just a one-in-three chance early last week, according to CME Group's Fed Watch tool.