According to local reports, French authorities have deployed multiple boats and helicopters throughout the vicinity to search for Agnes but had to end search efforts late Tuesday.
Mr Agnes, a father of three, joined Quiksilver in 1998, when the Australian brand began to expand internationally.
The CEO of Quiksilver's parent company is missing after his boat was found washed up on the southwest coast of France. He later radioed to port authorities that his return would be delayed because of thick fog.
The region is known for having occasional risky waves. But at 9.30am his empty boat was found washed up on the beach at La Graviere.
The CEO of Boardriders is still missing, and things took a turn for the worse later on Tuesday when his boat was discovered run aground and empty on a beach 15 miles south of Capbreton.More news: Gov. Abbott orders Texas Rangers investigation into allegations at Karolyi Ranch
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"The Boardriders family and entire surfing world are devastated by this news", the Huntington Beach company said.
The sea search continued after dark but the land search was suspended until Wednesday morning. Agnes served as the head of the company's France-based headquarters before taking control of the company in 2015.
Quiksilver's parent company, Boardriders Inc., now controls an extensive portfolio of action sports brands including Quiksilver, Roxy, DC Shoes, Billabong, RVCA, Element, VonZipper, and Xcel.
The World Surf League wrote on Twitter that news of Mr Agnes's disappearance was "deeply troubling".