SINGAPORE (Reuters) -The euro was subdued on Thursday after the widely expected collapse of the French government, stoking worries about the region's second-biggest economic power, while bitcoin galloped past $100,000 for the first time.

The world's best known cryptocurrency has been on a tear since November on expectations that Donald Trump's U.S. election win will usher in a friendly regulatory environment for cryptocurrencies.

It rose to as high as $101,626 in Asian hours and was last up 3% at $100,882, taking its year-to-date gains to 138%.

"If we are talking where we go from here, there's reason to believe this thing could keep going," said Kyle Rodda, senior financial market analyst at Capital.Com.

"Given the reduced regulatory risk, the continued appeal of non-fiat assets because of the perception of U.S. fiscal profligacy, and greater geopolitical risks, there are continued tailwinds that could support prices going higher."

The euro was fetching $1.052175, trading in tight ranges in Asian hours but was close to the two-year low of $1.03315 it touched at the end of November as traders brace for a long-winded reckoning for France.

French lawmakers passed a no-confidence vote against the government on Wednesday, as expected, throwing the country deeper into a crisis that threatens its capacity to legislate and tame a massive budget deficit.

"The fall of the government means that political uncertainty will persist and continue to weigh on business and consumer confidence," said ING economist Charlotte de Montpellier.

"Finding a new prime minister who will not face a motion of no confidence directly will be a very difficult mission. It is therefore likely that France will remain without a government for several weeks, if not months."

When asked if the European Central Bank would step in to help France should market turbulence intensify, the central bank president, Christine Lagarde, would only say that financial stability was a relevant factor in price stability.

In a parliamentary hearing on Wednesday, Lagarde said euro zone economic growth could be weaker in the months ahead and downside risks dominate the medium term outlook.

Traders are all but certain the ECB will cut rates next week and are pricing in 157 basis points of easings by the end of 2025.

In Asia, the South Korean won was stable as the nation's finance ministry said the government would activate 40 trillion won ($28.35 billion) worth of market stabilization funds after the chaos that followed President Yoon Suk Yeol declaring and then rescinding martial law.

South Korean lawmakers have proposed impeaching Yoon for the debacle that has rattled global markets. The won remains near its two-year low versus the dollar and is the worst performing Asian currency this year. It was last at 1,414.41 per dollar.

The yen strengthened a bit at 150.345 per dollar as traders ponder whether the Bank of Japan will hike interest rates later this month. Markets are pricing in 60% chance of a rate hike in December.

Over in the United States, investor confidence of a rate cut there held firm despite comments from Federal Reserve Chair Jerome Powell and a slate of economic data overnight that showed services sector activity slowed in November after posting gains in recent months.

Powell on Wednesday said the economy is stronger now than the central bank had expected in September when it began reducing interest rates, and appeared to signal his support for a slower pace of interest-rate cuts ahead.

The spotlight will be on Friday's non-farm payrolls report for November, with payrolls likely increasing by 200,000 jobs in the month after rising by only 12,000 in October, the lowest number since December 2020, a Reuters survey showed.

Markets are pricing in a 74% chance of a 25-basis-point rate cut from the Fed, up from 67% a week earlier, CME FedWatch tool showed.

The dollar index, which measures the U.S. currency against six rivals, was at 106.27. In other currencies, the Australian dollar was flat at $0.64241 after dropping about 0.9% in the previous session on weak data.

Sterling was little changed at $1.2709.