According to the petition, numerous areas of the city have been infected by the pests, especially those areas that are near lakes and rivers.
Earlier this year, it was also discovered that bedbugs had arrived in the French capital.
While the bites are harmless they can create severe skin irritation and itching.
According to a report by BFM television, 200,000 homes across France have been infested by the bugs.
Earlier in September the Bagatelle area of Toulose was infested by bedbugs in a period of only three days.
Citing Professor Antoine Berry, head of the parasitic and fungal infestations, the report says there has been a significant growth in the number of these pests in Northern Europe and America.
He pointed out that there was nothing exceptional about the pheromone in Toulouse and that it could easily happen in other towns at any time.
He also advised people not to panic as there is no evidence to suggest that the bedbugs can transmit diseases.
They are also difficult to get rid of once they have infested a building.
The Paris infestation occurred after the pesky critters infested New York City landmarks such as the Empire State Building, Carnegie Hall and even UN headquarters, bedbugs are becoming increasingly common in the City of Light, French fumigators say.
The tenacious critters, brown and barely 5mm long, often hitch rides in suitcases and then take up residence in mattresses, box-springs, bed linen and clothing. They tend to attack at night, leaving itchy, uniform bites.