"Equities certainly will trade down [with investors] moving out of equities into less risky assets - U.S dollar, Japanese Yen, government bonds, gold type assets," Grigor said.
"Last week was a pretty negative week on the US stock market anyway, with expectations U.S is going to raise rates despite the fact that growth was looking a little more difficult than people first thought. If you tie that in with that's happening with terrorist attacks in Paris, those two things are going to weight on stocks opening," he said.
The Paris attacks created some uncertainty about whether or not the U.S Federal Reserve would raise interest rates next month, he said.
"If they decide not to raise rates because of this, that adds some positivity into the market on the back of a really bad situation," Grigor said.
Many overseas analysts believe any economic impact will be short.
"As horrific as these events are - and this is truly awful - economic activity does tend to be pretty resilient," said Howard Archer, an IHS Global Insight analyst in the United Kingdom.
"At the end of the day, people have to get on with their lives."Sam Stovall, U.S. equity strategist for S&P Capital IQ, said the U.S. stock market will likely fall about 2 percent Monday, with larger declines in Europe.
But he said "it's not something that's going to throw the European economy into recession."
Based on the reactions to similar attacks in the past, Stovall expects stocks to begin recovering after about a week.
Shane Oliver, chief economist at AMP Capital, said the U.S. market took just over a month to recover from the Sept. 11, 2001, attacks, while the U.K. market rebounded in one day after the 2005 London bombings.