It has actually been envisioned by either prominent Gaullists (namely Alain Peyrefitte) and OAS members, who even discussed it, AFAIK, with moderates from the provisional Algerian Government in mid-1962, before the Pied-Noir exodus.
The idea, born after the failure of the 1961 putsch, was to "Israelise" not all of Algeria, but the Oranais zone (Oran being a city with a European majority). The Pieds-Noirs and Algerian Jews (who were French citizens by law, unlike the Muslims), were to gather in the Oran-Tlemcen-Sidi-Bel-Abbès zone, esure they would have a demographic majority, and organise themselves as a European stronghold, either within France proper (it was Peyrefitte's idea) or, more probably after a solid majority in France favored Algerian independance, as an independant country.
Actually, Oran was a rather industrialized zone (less that Algiers, arguably) and one of the more prosperous agricultural area in Algeria and, economically, the idea was not totally stupid. I also suppose that the leaders of the Oranian solution would have been reinforced by rebel officers, either condemned or ousted from the French army after the Putsch, and some right-wing radicals from France (and maby a few French colonists from Subsaharian Africa). Oh, and Harkis, too.
This said, a white rump Algeria would probably survive only for a few years, and probably not after 1975.
The country is bound to maintain a large, standing army to protect itself from a probably very hostile Algeria, from Muslim dissent within the country (assuming, of course, The Oranais didn't expelled, or worse, non-loyaist Muslims). Relations with France will be horrible. I'm pretty sure that the Oranais would back every Anti-Gaullist terroist organisation in France proper, and France, shifting to the 1960s industrial and European policies, would do everthing to distance from people who would be as popular as the radical Afrikaners in South Africa. The Oranais would have no support from the Socialist Bloc (duh), but, aside from ultra-conservative circles, I doubt the US would do anything favourable to a colonialist regime who would arguably be a troublesome element for Western strategy in the Middle East and the Mediterranean. The only help the Oranais could hope for would come from Francoist Spain, Portugal, South Africa and probably Israel (and maybe military dictatorships in Greece and Latin America). Morocco, having very bad relations with Algeria, might be a favourable neutral.
However, deprived from real economic perspectives, being a pariah state with, I suppose, few democratic features, under the permanent pressure of hostile neighbours and without any real, powerful ally to balance it (not to mention any legitimacy), especially after the Carnation Revolution in Portugal and Franco's death in Spain, I guess the country would collapse. You would have, either a transitional French mandate to set everything ready for retrocession to Algeria, or a violent collapse, the Oranais fleeing either to Isreal (for the Jewish population), Spain, maybe South Africa. I doubt many would reach France, given the hostiliy between the two countries.