Eurozone government bond yields fell in early trade on Monday, while the U.S. Treasury market was closed due to Columbus day.

Eurozone and U.S. bond yields nevertheless remained at elevated levels, reflecting solid economic growth in the U.S. and resilience in the eurozone, as well as inflationary pressures stemming from energy prices.

Concerns about fiscal problems in France linger, while the key event this week will be Wednesday's U.S. consumer-price inflation data as investors gauge how fast U.S. interest rates will rise.

"We think that higher bond yields fit the current economic climate of high growth and high demand for capital," said Joost van Leenders, senior investment strategist at Van Lanschot Kempen, in a note. "Concerns about government budgets play a role here, the situation in France being especially worrying," he said.

The French government's budget plans for 2027 envisage a reduction of the deficit to 5% of the gross domestic product in 2027. However, there are concerns about whether approval for substantial budget cuts can be secured from a fractured parliament, particularly ahead of next year's presidential elections.

"France will therefore continue to be a source of uncertainty for some time to come," van Leenders said.

"Focus will continue to be on developments in France with parliament set to start debating the revenue side of the budget this week," said Silje Bue, strategist at Danske Bank, in a note.

The 10-year German Bund yield fell 2.6 basis points to 3.463%, while the 10-year French OAT yield declined 1.5 basis points to 4.847%, according to Tradeweb.

In the U.S. Treasury market, Wednesday's consumer-price inflation data for September will provide important information ahead of the Federal Reserve's next interest-rate decision on Oct. 28.

Analysts forecast a rise in the headline inflation to 3.7% from 3.4% previously, according to The Wall Street Journal's poll of analysts.

In September, the Fed raised interest rates by 25 basis points. Markets currently price in a small 18% probability of another rate hike at this month's meeting, though they anticipate a total of three hikes over a 12-month horizon, according to LSEG.

Some long-term investors see potential appeal in eurozone and U.S. Treasurys with yields at such high levels, but they remain cautious for now.

Morgan Stanley strategists see value in U.S. Treasury duration but favor waiting until after the Federal Reserve's Oct. 28 interest-rate decision and the Nov. 3 midterm elections.

"Midterm policy outcomes should matter little for Treasurys, but the vote's passing may change Iran's approach to the Strait of Hormuz and the energy trend," they said.