The law, which was passed and adopted by France's parliament last month, required online platforms and search engines to remove hateful or terrorist content within 24 hours of it being posted, risking fines of up to €1.25 million.
She has denied the allegations and said she would file a defamation claim.
The law allows for fines of up to €1.25 million but critics say it would curtail the democratic right to freedom of expression.
A Facebook post showing a photograph of a gay couple kissing triggered hundreds of online hate comments, including death threats. The European Court of Human Rights ruled against Lithuania for failing to prosecute perpetrators.
What happened "will be shown to be directly related to the hate that people are bombarded with every day on the internet and elsewhere," the lawyer said.
A Belgian MEP and a hate speech advisor debate over who's right.
Online hate is rampant, but a French bill in development for this year is trying to limit it. Here's how.
Muslim mayor Sadiq Khan reads out expletive-laden hate speech in the video, which Has so far attracted 170,000 views on Facebook.