Digne, 25, has been linked with the Toffees for several weeks and has been permitted to "finalise his departure" ahead of a €25 million (£22m/$29m) move.
He was part of France's squad at the 2014 World Cup, but found himself overlooked for the country's triumphant 2018 campaign.
Digne would likely serve as the heir to veteran Leighton Baines, with Everton having been linked to numerous left-backs this window.
The Toffees are looking to pick up the pace in a transfer period that has been slow for them following the appointment of former Watford manager Marco Silva.
Silva has seen multiple players depart the club, with Wayne Rooney and Ramiro Funes Mori among them.
The Premier League transfer window slams shut August 9, but things may be picking up as the club finalised the signing of one of Silva's former Watford players, Richarlison, last week to a five-year contract.
Everton have also featured in the race to sign Digne's team-mate Yerry Mina, with the Colombian international also struggling to break into the team under Ernesto Valverde.