Israel bought Gloster Meteor F4s so GB wasn't out of the picture. But then their atempts at buying F-86s were thwarted, either in the USA or Canada. By 1956 they would be very pissed off. They also tried buying J-29s but sweden neutraility prevented that.
As for France... without Dassault, the AdA would have bought SO-6020 Espadon (swordfish)
https://en.wikipedia.org/wiki/Sud-Ouest_Espadon
The Espadon wasn't a bad machine but it was plagued with weight growth, lack of engine power (Nene) and air intakes issues (unlike the Ouragan straightforward intake) In the end by 1954 one of the 4 build was the first supersonic French aircraft, with the help of a big rocket engine.
After Espadon, what ? the Trident will remain a dead end. Unlike the SE Durandal of 1956
Both all weather and bomber missions would go to the SNCASO Vautour
So in the end the public companies might pull it, but it will be slower and much less glamourous than Dassault.