PARIS — French regulators said Tuesday that they had asked prosecutors to investigate Microsoft’s Skype unit over its failure to register as a telecommunications operator in accordance with local law, raising the question of what constitutes a telephone company in the age of Internet-based communications.

The regulator, known by its French acronym Arcep, said that it had, “on several occasions," asked Skype Communications, which is based in Luxembourg, “to declare itself an electronic communications operator,” and that the company had not acted.

A company acting as a telecommunications operator incurs certain obligations, the French agency said, notably that “of routing emergency calls and putting in place a means for allowing legal wiretapping.”

Skype and other Internet phone services use a system called voice-over-Internet protocol, or VoIP, to enable conversations and video meetings over the Internet. The service, which Microsoft acquired from eBay in 2011 for $8.5 billion, says it has hundreds of millions of users worldwide.