Eric Bormann killed the one-and-a-half-year-old tigress called Mevy after people spotted her wandering around the French capital's 15th arrondissement on Friday.
Police questioned Bormann for several hours after the incident, and an investigation has been launched into whether lives were put in danger.
However, the head of the Bormann-Moreno circus claims foul play, and has asked police to investigate
"I'm the one who takes care of my tigers," Bormann, who also serves as the lion trainer, told AFP.
"There is a whole security protocol to respect with big cats," he said, explaining the animals were in a cage secured by another enclosure.
"In our security protocol, if a beast escapes -- which has never happened in the 40 years I have been in Paris -- it remains locked. It is a cage within a cage."
Bormann claims that on Friday at around 6pm, when he opened a separation door to clean the tigers "a tigress was out because a door, usually locked, was open".
"We suspect a malicious act. There was a chain with a padlock, and the chain was cut."
Two-hundred kilogram Mevy, who had been bottle-fed by Bormann, was gunned down by her ringmaster using the firearm he is required to carry by law within a few minutes of her escape.
He added that the idea of using a tranquillizer gun was quickly ruled out because of the time it takes for the sedatives to work.
The circus, which has several tigers, had just set up and planned to open its doors to the public on December 3rd.
The Brigitte Bardot Foundation -- named after the actress and animal rights activist -- said it was "scandalised by the slaughter of the tiger" and called on the government to ban the exploitation of animals in circuses.