Neville, who had previously never worked in women's football and whose management experience extended to one game as an interim for non-league Salford City, was under pressure after his appointment earlier this year was heavily criticised.
Further first half goals from Manchester City midfielder Jill Scott and Seattle Reign forward Jodie Taylor, who won the Golden Boot at Euro 2017, saw England open up a 3-0 cushion.
The scoring continued when Chelsea winger Fran Kirby netted a fourth immediately after the restart, with France, only three places below England in the FIFA World Rankings, shellshocked.
A 77th minute strike from classy French forward Gaetane Thiney was scant consolation.
Neville, who inherited control from interim coach Mo Marley after the sacking of former boss Mark Sampson last year, was unsurprisingly delighted to get off to such a good start.
"I was a little bit nervous before the game, I had a few butterflies, but my players didn't, that's the most important thing," he told BBC Sport afterwards.
"There is great expectation and I love that expectation. On the bus on the way to the ground it felt right. It felt right standing in the technical area and the most important thing is the players are enjoying the raised expectations and the higher profile."
France won the last SheBelieves Cup and are considered one of the top women's international teams in the world alongside, the United States, Germany and now England, with the four nations meeting in the invitational tournament each year since 2016.
The United States won their opening game against Germany by a single goal from Megan Rapinoe, a member of Juan Mata's charitable Common Goal movement.
Neville will take charge of his second England game on Sunday night when the Lionesses face Germany, followed by a final outing against the American hosts on 7th March.