https://www.globalsecurity.org/wmd/systems/b-66.htm
FAS nails it well: both B-57 and B-66 were stopgaps and never really satisfyied the Air Force (although they found interesting missions in the 60's: RB-57F and EB-66).
I think a good POD might be the end of the Korean War. The Vautour flew in October 1952.
At the end of the Korean war, both B-57 and B-66 programs are cancelled.
By the fall of 1952 Chuck Yeager and Richard Boyd (later the father of the F-16 LWF: the fighter mafia) are in France to flight test Dassault Mystères II and IV (it really happened OTL). In the process the two pilots stumble on the Vautour and phone the Air Force "I got your bomber to replace B-57 and B-66 !".
Also: France was a major user of A-26 Invaders in Indochina, and just like the Air Force, they want to replace them.
So by late 1953 SNCASO gets in touch with a US Company (pick your choice !) and sell them a licence to build a much improved Vautour.
First, the engine: America had plenty of excellent engines to replace the Atar. J52 might do the job. Or J65. Or J57 (all of them without afterburner).
Of the three, the closest from the Atar is the J52. It really fits like a glove. Plus A-4 and A-6.
Then the avionics. Gone is the Norden, all-weather avionics are fitted. Probably a LABS, too.
As for the missions, the US Vautour will have many of them: tactical and strategic reconnaissance, electronic warfare, low level bombing, aerial refueling... its career will span into the 70's and the Vietnam war.
And of course Israel as per OTL.
Note: India used Ouragan and Mystere IV.
South Africa used Canberras and Buccaneers: if the Vautour is good enough, no need for the latter. They will fought along Mirage IIIs and Mirage F1s.
As for Argentina in the Falklands: France and the United States will probably embargo any spares, still the Vautours could indeed be use as tankers.
Vietnam will be "fun" with Australian and U.S Vautours fighting all kind of missions. The pair of 30 mm guns will get a couple or trio of MiG kills. ECM Vautours, perhaps anti-radar strikes with Shrikes and Standards ARMs.
now if you are a little more ambitious... with its pair of J-52s and large internal volume... the Vautour may kill the A-6 Intruder...
I checked their respectives sizes, the Vautour is only a little smaller than an Intruder (51*51 ft versus 55*55 ft, their wing areas are quite similar).
How about that.
also if the F-100 youth is as troubled as OTL, Vautours may fill the gap.