French government bond yields rose on Monday, staying at elevated levels not far below Friday's multiyear highs, amid building concerns over the country's indebtness.

Treasury yields eased meanwhile after weaker-than-expected U.S. nonfarm payrolls data caused markets to trim expectations for another U.S. interest-rate increase in October.

French 10-year government bond yields increased 4.8 basis points to 4.904% in early European trade. They hit a peak of 4.993% Friday, their highest since 2002 amid concerns that the government's recent budget proposal will struggle to be approved by a fragmented parliament. By contrast, 10-year German Bund yields fell 2.0 basis points to 3.435% as investors sought the safety of German bonds.

The French-German 10-year bond spread stood at 146.30 basis points, having spiked on Friday to a near 15-year high of 158.67 basis points.

"In European government bond spreads, we would not attempt to catch the falling knife yet, as an agreement on the French budget is a long way off and the European Central Bank is unlikely to act on spreads yet," Commerzbank rates strategist Hauke Siemssen said in a note.

Fiscal concerns should keep yields under sustained pressure, except for Bunds, he said.

Treasury yields fell after U.S. nonfarm payrolls rose just 29,000 and the unemployment rate increased to 4.2% in September, according the U.S. Bureau of Labor Statistics on Friday. Economists in a WSJ survey had expected an 84,000 increase in payrolls and the unemployment rate to remain steady at 4.1%.

The yield on the 10-year Treasury fell 1.3 basis points to 5.264%, having reached a 24-year high of 5.344% on Thursday, according to Tradeweb. The 30-year equivalent dropped 0.7 basis points to 5.623% after hitting a 24-year high of 5.693% Thursday.

"The [jobs] report supports our view on the Fed where we see the next hike in December and just one more hike in this cycle," Jefferies economist Mohit Kumar said in a note.

"Of course, we admit that the view of just one more hike is contingent on our still optimistic view of the U.S. Iran war," he said.

Following Friday's jobs data, markets priced an 18% chance of the Fed raising rates in October, compared to over 70% last week, according to LSEG.