It said that following last week's EU summit, it "has concluded that a 'comprehensive solution' to the eurozone crisis is technically and politically beyond reach."
The warnings came at the end of a day full of negative news for Europe. Ireland's economy contracted much more than expected in the third quarter, Spanish regional debt rose sharply over the past year, and EU officials admitted that talks to get Greece's private creditors to take losses on their bonds were not going as well as hoped.
The affirmation of France's rating and the Italian government's survival of a confidence vote were rare bright spots in a week of dire financial news for Europe.
After trading higher most of the day, European stocks closed lower. Britain's FTSE shed 0.3 percent to 5,387.34 and Germany's DAX lost 0.5 percent to 5,701.78.
France's CAC-40 closed 0.9 percent lower at 2,972.30 - its losses were driven in part by a report from the national statistics agency predicting a recession in the country over this quarter and the next. Fitch's affirmation of the country's rating came only after markets closed.
Investor sentiment had been stronger earlier in the day, as traders focused on an improvement in U.S. economic indicators.
This week, U.S. government data showed the number of people applying for unemployment benefits last week was at its lowest since May 2008. That's a sign that layoffs are easing, a first step toward bringing down the unemployment rate, which currently stands at 8.6 percent.
Traders were also encouraged by a report from the Federal Reserve of New York that its index measuring regional manufacturing jumped to the highest level since May. That was far more than economists were expecting. A similar report from the Philadelphia branch of the Fed also increased more than analysts anticipated.
Early gains in Wall Street were trimmed by the concerns in Europe. The Dow Jones industrial average dipped 0.2 percent to 11,848.15, while the S&P 500 gained 0.1 percent to 1,217.24.
The euro was steady at $1.3013, as was the dollar against the Japanese yen, at 77.85 yen.
In Asia, Japan's Nikkei 225 index closed 0.3 percent higher at 8,401.72. South Korea's Kospi rose 1.2 percent to 1,839.96 and Hong Kong's Hang Seng added 1.4 percent to 18,285.39. Benchmarks in Singapore, Taiwan and Indonesia also rose.
Mainland China shares ended a six-session losing streak, with the benchmark Shanghai Composite Index gaining 2 percent to close at 2,224.84.
Analysts stopped short of calling the gains a recovery, as trading was light ahead of the holidays.
Signs emerged that the Chinese central bank may have intervened in the currency market by offering dollars to support the Chinese yuan, which has been weakening in recent sessions. That raised speculation that authorities may plan more market-boosting measures.
The yuan strengthened to a record 6.3294 against the U.S. dollar, but later eased to 6.3446. Weakness in the yuan could raise tensions with countries such as the U.S. that complain it is already undervalued.
Benchmark oil for January delivery was up 26 cents to $94.13 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell $1.08 to finish at $93.87 per barrel on Nymex on Thursday.