Four weeks after the 2021 Six Nations, the Rugby Football Union sent out an email.

More psychological help for the players. Referees to give advice on improving discipline. An integrated analytics model.

It was hardly root-and-branch stuff. More some gentle topiary. After another underwhelming Six Nations was rounded off by defeat by France on Saturday though, some are calling for the most dramatic cut of all: the departure of Eddie Jones.

Captain Courtney Lawes came out to defend his coach on the eve of the match, describing speculation over Jones' job as "ridiculous".

But it is certainly not the results on the pitch that make a coaching change seem far-fetched.

England finished third in this year's Six Nations, but their record - two wins, three losses - is the same as 12 months ago.

They scored eight tries, five of which came against bottom side Italy, four fewer than they managed in 2021.

They also broke fewer tackles than any other side, despite a promise to loosen the reins and show off a more attacking style.

The gripes among England fans are growing. Parts of the media have turned, calling openly for Jones' immediate departure.

The theory is plausible: a new coach to jump-start the team before next year's Rugby World Cup.

It is not too late. This is the point in the last cycle when South Africa swapped the floundering Allister Coetzee for Rassie Erasmus. Eighteen months later, Siya Kolisi was hoisting the trophy in Yokohama.

Australia made the final in 2015 after ditching Ewen McKenzie and bringing in Michael Cheika the previous year.

France won through to the 2011 showpiece effectively without a coach at all, as relations between Marc Lievremont and his players crumbled.

But reality is messier than theory.

The England head coach role may be the biggest toybox in rugby, given the resources and playing numbers available, but elite coaches are not queuing up to play.

Former Wales and British and Irish Lions coach Warren Gatland, now with the Chiefs in New Zealand, would have to row back on a promise to never take charge at Twickenham.

Exeter's Rob Baxter intends to honour a contract at Sandy Park through to next year.

Shaun Edwards - France's English defence coach - has more than two years left on his deal and would surely be loathe to walk away from such an exciting project.

Scott Robertson, the Crusaders' all-conquering coach, may prefer to see if the national team job in his native New Zealand job comes his way rather than swap hemispheres.

Steve Borthwick, a former England captain and assistant coach, might be likeliest given the way he's transformed Leicester Tigers in a short time. But it would be giddy promotion given his relative lack of Test and head coaching experience.

Erasmus, for all his coaching qualities, surely comes with too much baggage after his part in a rancorous series against the British and Irish Lions last summer.

None would be cheap. Not least because, presuming there are no break clauses in the small print, the remaining 18 months of Jones' current contract would need paying out.

The Rugby Football Union has little wriggle room even if they did want to make a change.

Covid costs left a £120m hole in its finances. It cut 119 jobs to balance the books. The highest-profile redundancy of all would hit the bottom line further.

And Jones is not going to make it easier for the RFU by walking away.

"That is not a question I need to answer," he said when asked about his future in the wake of the France defeat.

"I just do my job. It's a question for other people.

"All I can say is that we know what we're doing, that we're on the right track and the team will keep progressing."

So, the Rugby Football Union would have to take a big gamble, one it can ill-afford, with a level of risk it has rarely shown appetite for previously.

Sticking seems likelier than twisting.

Even more so when the RFU came out on Sunday citing the "positive steps" they had seen during the Six Nations and assuring Jones of their "full support".

Jones and England will muddle along for now in a marriage of convenience and hope the magic emerges again.

There are positives to build on.

Maro Itoje burnished his status as the team's bona-fide world-class player. Ellis Genge has come a long way at loose-head prop, scuttling Ireland's Tadhg Furlong in the scrum last week and trucking the ball up time and again in the Stade de France.

Marcus Smith's kicking from hand and tee showed there is more to his game than the eye-catching jinks and darts. Joe Marchant, Jamie George and Harry Randall staked claims for the summer tour to Australia.

By then, old stagers Owen Farrell, Manu Tuilagi and Jonny May should be back from injury to restore some of the winning habit.

But more than personnel, the team needs a plan. France and Ireland, the tournament's two best teams, have thick playbooks and patterns they can run in their sleep.

England instead seem to rely on a moment of genius from Smith or centre Henry Slade. Playing heads-up rugby is all very well, but against well-organised defences licence to run the ball, on its own, is worth little, at least the first few phases.

When the inspiration fails to emerge, England fall back on attrition, hoping to wear down defences and, all too often, running out of steam themselves.

Jones has pulled England out of significant dip in form before, recovering from finishing fifth in the Six Nations in 2018 to come within one (admittedly one-sided) match of winning the 2019 Rugby World Cup.

Six and a bit years into the job does he still have the tricks to inspire his team and innovate tactically?

A series against his native Australia, where he chalked up a whitewash series win in his honeymoon period with England in 2016, will be testing.

We will soon find out if he has.

Jones' highs and lows as England coach