They would then visit their house, carry out phoney control services, including spraying aerosols they claimed were acting as a fumigator, before overcharging for treatment products.
They offered an ointment they said would keep the bugs away from human skin. In fact, it was a simple eucalyptus-scented cream.
The authorities said 48 people had been scammed altogether, many of whom were women over 90.
There has been a rise in bedbug infestations across France in recent months.
In October, France shut several schools over what was thought to be an infestation of bedbugs and the government held a series of emergency meetings.
The blood-sucking insects were reportedly spotted on the Paris metro, high-speed trains and at Charles de Gaulle airport. Individual cases were not confirmed by the authorities.
But entomologists and health experts have cautioned that the outbreak has also led to a rise in false sightings and unwarranted hysteria.
Victims of this bedbug scam would be charged between €300 and €2,100 (£257 and £1,800) by the two alleged perpetrators as they took advantage of this hysteria.
Police said they had received a total of nine formal complaints for suspected fraud.
The suspects were then placed under surveillance and arrested as they left the home of an alleged victim in Strasbourg.
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