The FTSE 100 lost 0.3% to 7,357.15, while Germany's DAX gained 0.3% to 13,199.34. The CAC 40 in Paris also rose 0.3%, to 5,889.60. U.S. futures augured a slow start, with the S&P 500 dropping 0.3% and the future for the Dow Jones Industrial Average losing 0.2%.
Britain is to officially leave the EU at 11 p.m. local time Friday, midnight in Brussels (2300 GMT, 6 p.m. EST). The departure comes 3½ years after the country voted by a margin of 52%-48% to walk away from the club that it had joined in 1973.
But that just begins an 11-month transition period as the UK and EU negotiate agreements on trade, security and other issues. Prime Minister Boris Johnson's government hopes to negotiate a deal with the EU alongside a free trade agreement with the United States.
With other momentous events grabbing attention, the news that France's economy contracted 0.1% in the last quarter appeared to have little immediate impact.
For much of the world, the main focus was on the ripple effects of the outbreak of a virus first found in central China that has killed at least 213 and sickened nearly 9,700.
Shares were mostly lower in Asia after the World Health Organization declared the pandemic that has spread from China to more than a dozen countries a global emergency. Markets in mainland China remained closed as the U.S. warned against all travel to China following the WHO's announcement.
Japan's Nikkei 225 index rose 1% to 23,205.18, while the S&P ASX/200 edged 0.1% higher to 7,017.20. Hong Kong's Hang Seng fell 0.5%, to 26,312.63, while the Sensex in India edged 0.1% higher to 40,939.19. Taiwan's benchmark picked up 0.6%, while South Korea's Kospi skidded 1.4% to 2,119.01. Shares also fell in Jakarta and Kuala Lumpur.
A monthly survey of manufacturers in China showed factory activity weakened, but it did not reflect the latest developments from the virus outbreak.
Overall, stocks have given up some ground after a strong start to the year amid uncertainty over the virus outbreak. Still, the major U.S. indexes remain on track to end January with gains.
The WHO's move to declare the outbreak a global emergency Thursday came after the number of cases spiked tenfold in a week. The declaration means the WHO sees the virus as a risk to other countries that requires an international response.
Benchmark crude oil rose 54 cents to $52.68 per barrel in electronic trading on the New York Mercantile Exchange. It fell $1.19 to settle at $52.14 a barrel on Thursday. Brent crude oil, the international standard, picked up 47 cents to $57.80 per barrel. It dropped $1.58 to close at $58.33 a barrel overnight.
In other commodities trading, gold dropped $5.60 to $1,577.90 per ounce, while silver fell 13 cents to $17.86 per ounce and copper fell 3 cents to $2.52 per pound.
The dollar was flat at 108.98 Japanese yen. The euro fell to $1.1032 from $1.1033.