Story highlights The French are more likely to back missile strikes than Germans or British

Even in France, only one in three supports strikes on Syria

Half of British people support military intervention if the U.N. approved it or found chemical weapons use

The agency ComRes polled 500 people online in each of the three countries

As the United States and its allies wrestle with how to respond to the possibility that the Syrian regime used chemical weapons against its own people, a new poll for CNN finds Washington's European allies distinctly lukewarm on military intervention.

The French are more willing than the British or the Germans to launch missile strikes on Syria, but even there, only one in three people backs bombing. One out of five Germans is in favor of missile strikes, while the number is even lower in the United Kingdom, at 16%.

France's parliament is due to debate possible action on Syria on Wednesday. Last week, Britain's House of Commons rejected even the possibility of a military strike on Syria, in a vote that shocked Prime Minister David Cameron and raised questions about the so-called "special relationship" between Washington and London.

President Obama is lobbying members of Congress to back military action against Syria, where President Bashar al-Assad is accused of using chemical weapons on August 21. President Obama had said in the past that the use of chemical weapons would be a "red line."

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The survey, conducted by the polling agency ComRes for CNN on August 30 -- after the British vote -- found economic sanctions to be the most popular course of action in all three countries polled.

More than half of Germans -- 55% -- backed tightening economic sanctions , while 46% of British people and 39% of French people did.

Poll respondents were allowed to choose more than one option from a list of "most appropriate responses," which included tightening sanctions, establishing a no-fly zone over Syria, striking Syria with missiles, invading with a ground force and doing nothing.

More than one in five Germans favored doing nothing (22%), as did more than one in four French people (27%) and nearly one in three British people (30%).

But about half of British people said it would be appropriate for their country to engage in military intervention if the United Nations found evidence Assad had used chemical weapons or if the U.N. explicitly sanctioned the use of force. Just under half of German people agreed, as did 35% of French respondents.

The poll did throw up some surprising paradoxes. Germans were the most likely of the three countries to say they should not engage in military intervention under any circumstances -- but also the most likely to say that military intervention could help stop Assad from using chemical weapons in the future and enable positive regime change.

The poll was conducted online on August 30, sampling 500 adults each in France, Germany and the United Kingdom. Data were weighted to be demographically representative by age, gender and region of all UK, French and German adults aged 18 and up.

The margin of error is plus or minus 4.38 percentage points.

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