The call came as false rumours about hostages, down to detailed specific locations, came from social media accounts with credible-sounding pedigrees.
This turned out to be absolutely incorrect, but was also propagated by news organisations.
But French Interior Ministry spokesman PH Brandet was quick to stamp out the false rumour, saying there's no hostage situation.
There were also many messages about a supposed second attack in Paris, which turned out to be a spectacular bonfire against the backdrop of the Eiffel Tower when a Bastille Day fireworks truck caught fire.
While some took the Gendarmerie request to heart, such as US investor Adam Khan, who told users this was sound advice from the police as most early information would be inaccurate, there were many who did not heed the suggestion.
Some even posted unsavoury responses directed at the police request.
Internet trolls flooded the Gendarmerie account with fake messages about missing people, including repeating the bizarre hoax about the mysterious man who had supposedly died in the Air Egypt crash on May 19, then again in the Orlando, Florida, shootings on June 12, and later linked to a police shooting in Mexico on June 19, this time as being the official ordering police to shoot.
France 24 earlier in the month managed to trace the individuals spreading the messages, all from Mexico, some admitting that they knew the man personally and that he had cheated them out of money, ranging from fairly small sums up to about $1000.
The French national broadcaster on July 5 located the person in question, who admitted he was caught up in legal proceedings and a vendetta over debt.
He told France 24: "My photo is everywhere because of someone who started it as a prank after a legal dispute. I never reported the people who did this to me because, in Mexico, nothing ever happens in these kinds of cases.
"Now, my photo has appeared in several stories that were widely shared on Twitter. I contacted several media outlets like the BBC and the New York Times and asked them to delete my photo but they never responded."
The broadcaster decided not to publish his real name
French lawyer Fabrice Lorvo told the station that French law on cyber-harassment was still a work in progress, and that while the first person who tweeted such a photo in France could face serious criminal and civil consequences, the development pointed to a bigger problem.
"It shows that traditional media outlets are more and more influenced by social media. Numerous websites shared this man's photo without verifying its origins!"
France24 pointed social media users to their extensive guidelines for verifying photos and videos on social media.
In other cases the misinformation following terror attacks are well-intentioned and not driven by malicious trolls, but nonetheless false.
At the time of the Paris attacks in November last year, more than 10 million tweets about Paris were posted between the Friday and Saturday, including the photograph below, purporting to be Parisians flooding the streets then, with signs declaring they are "Not afraid".
But, it turns out the photograph was actually taken nearly 10 months earlier, following the January 7 Charlie Hebdo attacks.
At the time of the Dallas attacks a few days ago, many media personalities retweeted the NYC public radio On The Media blog's "Breaking News Consumer's Handbook", with tips for members of the public on how to verify what they are reading.
On The Media explained in 2013 that rampant misreporting following shooting incidents were so predictable that they unintentionally developed a formula for covering them.
"We look at how all the bad information came out. We suggest ways that the news media could better report breaking news. This time, we're doing something different.
"This is our Breaking News Consumer's Handbook. Rather than counting on news outlets to get it right, we're looking at the other end. Below are some tips for how, in the wake of a big, tragic story, you can sort good information from bad. We've even made a handy, printable PDF that you can tape to your wall the next time you encounter a big news event."
A project funded by the EU to the tune of 4.3 million euro to tackle the wider problem of speculation, controversy, misinformation, and disinformation across social networks and online media is Pheme, named after Pheme - the Greek goddess of fame and rumours, but also coined to to describe memes which are enhanced with truthfulness information.
Pheme, which now has research partners from seven different countries, aims to use an interdisciplinary approach to combine big data analytics with advanced linguistic and visual methods.
Some of the project's early wins relate to analysing how close those posting messages are to the location of the actual events they are describing.
Pheme media partner Swissinfo has created a short video to explain its role in the project and how the Pheme dashboard currently being developed will help journalists to verify user-generated content on social media. They spent several months tracking news stories online, analysing tweets for rumours, and checking if claims turned out to be true or false - all to help other Pheme partners develop and train algorithms.
The project's text and data-mining partner Ontotext has already scored an early win, correctly predicting the outcome of Britain's Brexit referendum on June 13, 10 days before the actual votes were cast, all based on analysing tweet frequencies and locations.
The Pheme project aims to release many of the veracity intelligence algorithms as open source. Its results will eventually be applied to digital journalism and will also be suitable for direct application in medical information systems.
The project was started on January 1, 2014, and influenced strongly by the wild disinformation spread following the 2011 riots in England.
"The London Eye was on fire during the 2011 England riots! Or was it?
"Social networks are rife with lies and deception, half-truths and facts. But irrespective of a meme's truthfulness, the rapid spread of such information through social networks and other online media can have immediate and far-reaching consequences," the project said.
"In such cases, large amounts of user-generated content need to be analysed quickly, yet it is not currently possible to carry out such complex analyses in real time."
Pheme says social media poses three major computational challenges, dubbed the 3Vs of big data: volume, velocity, and variety.
The EU project is focusing on a fourth crucial, but hitherto largely unstudied, challenge: veracity.