France has seen huge protests against the bill over the last six months, and some smaller ones in favour of the proposed law.
In recent weeks, some far right groups have also taken up the issue.
The one-page letter to Socialist Claude Bartolone, the Speaker of the National Assembly, reads: "Our methods are more radical and direct than the protests, you wanted war, you have it."
Senator Esther Benbassa says she has received threatening phone calls, e-mails and letters and her car was vandalised earlier this month, she believes because of her support for the bill.
Erwann Binet, a Socialist MP who supports the bill, has been forced to cancel planned debates for security reasons after being heckled by far-right militants.
Although a majority of French people support gay marriage, adoption by gay couples does not have majority support.
Rights groups report a rise in verbal and physical assaults against homosexuals which they believe is linked to the current tension over the bill, though the manif pour tous, the main movement against the bill, has repeatedly denounced homophobia
The letter to Claude Bartolone was sent by the same group who recently sent threatening letters to two journalists and to the investigating magistrate who placed former president Nicolas Sarkozy under formal investigation in connection with the so- called L’Oréal affair.