With US tech stocks sliding as interest rates and recession fears rise, the fortune of Tesla owner Mr Musk briefly fell below that of the Arnault family.
But later in the day, Mr Musk was back on top at $184.9 billion, followed by Mr Arnault and his family at $184.7 billion.
Mr Arnault had also topped the Forbes list for several hours in 2021.
His LVMH group, with includes dozens of brands including Louis Vuitton, Givenchy and Kenzo, has continued to post strong revenue and profit growth despite the latest global economic headwinds.
Mr Musk's fortune is primarily tied to the share price of Tesla and the entrepreneur has been at the centre of controversy after having taken over Twitter in late October.
He also owns space exploration company SpaceX.
The other major wealth ranking compiled by financial data provider Bloomberg also has Mr Musk and Mr Arnault running nearly neck and neck.
Bloomberg's ranking, calculated after US markets closed on Tuesday, had Mr Musk in the lead at $178.9 billion, followed by Mr Arnault at $165.1 billion.
Agence France-Presse contributed to this report