Jamaica coach Lorne Donaldson hailed their goalless draw at the Women's World Cup against strongly fancied France as the greatest result in the country's football history on Sunday.

In only their second Women's World Cup, and having lost all three games at the 2019 edition, his side celebrated at the end as if they had won.

The only sour note was Manchester City striker Khadija Shaw being sent off near the end, meaning she misses the next match.

"I would say it's the number one result we have had so far, men or women -- I would put it there," Donaldson said after Jamaica scrapped their way to a 0-0 draw in the Sydney rain.

"You're playing a team like France who are just fantastic. I mean, just looking at the rankings, you would say that result on this stage has to be number one."

France, ranked fifth to Jamaica's 43, were widely expected to advance to the last 16 as Group F winners but after this stalemate to open their title bid that is now in doubt.

Jamaica produced a stirring rearguard action to repel waves of second-half attacks and frustrate the French.

Played in front of 39,045 fans at sodden Sydney Football Stadium, it was a physical and free-flowing affair with three players booked and Shaw shown a red card in the dying minutes for a second silly tackle.

It means Shaw will miss their game against Panama.

Kadidiatou Diani almost broke the deadlock in the 88th minute when her header clattered off the bar for Herve Renard's side.

But France were ultimately undone by poor finishing and the courage of a side ranked 38 places below them, spelling a disappointing start for a French team tipped to go far.

"They gave us a good run for our money... but I think we need to keep a cool head. I think we deserved to win, I have full faith in my girls," said Renard.

"It's easy to be negative but I'm focusing on the positives," he added. "We have just started this competition."

France were hampered by injuries and kicked off without regular defenders Elisa De Almeida and Selma Bacha, who are expected to be fit to play Brazil on July 29.

Estelle Cascarino and Sakina Karchaoui lined up at the back instead, with Maelle Lakrar and veteran captain Wendie Renard to deal with the danger posed by the powerful Shaw, who scored 31 goals for City last season.

The Reggae Girlz started positively with Renard and Shaw needing treatment for an early clash of heads in a feisty opening.

Both recovered with Jamaica the better side in the opening 20 minutes, forcing France into some frantic defending.

Shaw was a constant nuisance and France striker Clara Mateo was booked in the 13th minute for hacking her down.

Despite their early pressure Jamaica had few clear-cut chances and it was France who nearly opened the scoring when Mateo found Diani in the box. Her shot hit the target but Tottenham Hotspur goalkeeper Rebecca Spencer turned it behind.

Shaw also went close with a blistering strike from a free-kick -- Jamaica's best effort of a first-half which France finished strongly and saw Shaw and teammate Atlanta Primus also go in the referee's book.

France were a different team in the second half as rain swept down, dominating possession and finding more space to launch attacks, constantly threatening as the pace picked up.

They had a hatful of chances and there were countless goalmouth scambles, but Jamaica valiantly held on for a precious point.