Edwards has made a big impact since he was appointed Les Bleus' defence coach in May 2019 after a hugely successful spell with Wales under Warren Gatland.
The Englishman's influence in the Fabien Galthie era has been clear to see and France travel to Twickenham on Sunday (AEDT) with high hopes of ending an 11-year wait for a Six Nations title, having beaten Italy and Ireland before a coronavirus outbreak in its camp led to the clash with Scotland being postponed.
Betsen knows all about Edwards's coaching ability after working under the former rugby league star at Wasps and the ex-France flanker thinks he should be a contender to take charge of his country when Eddie Jones's reign ends.
"Shaun Edwards demands the highest standards every day," Betsen, who won 63 international caps, said. "He is passionate, emotional, he is a winner and wants to share the recipe of how to manage players. Also, it is very important to French people that he has made an effort to improve his French.
"He has got something very special. He had great success with Wales, he knows what he needs to do and how to go about doing it.
"He would deserve the opportunity to coach England and he would bring incredible passion as a proud Englishman.
"I am surprised Shaun has not been employed by England, but maybe people don't know what he is about. Obviously I am happy as a Frenchman, though, leave him with us and sort your own problems out!"
The Red Rose goes into "Le Crunch" smarting from a controversial 40-24 defeat to Wales that shattered its hopes of retaining the title.
Pascal Gauzere admitted he was wrong to award Wales two first-half tries in that loss for the defending champion in Cardiff, but Betsen says the French official was not to blame for England's defeat.
He said: "The referee admitted to making mistakes and we all make mistakes. As players, we also make a lot of mistakes.
"Last November nobody said anything when England benefited from refereeing decisions when they won the Autumn Nations Cup final against France.
"You have to respect the decisions of the referee and can only control your own performance."