This question inspired by 1940: et si la France avait continué la guerre..., in which the Third Republic does actually evacuate to Africa to continue the war from there.
To a certain extent, the French government did start a process of evacuation of key assets to safer zones. The French fleet went to either southern French ports like Toulon or to the North African colonies. French aircraft likewise went to these refuges away from the advancing front where they could be preserved as a nucleus of future French military power. But such evacuations fell far short of plans for a national redoubt either in Brittany or North Africa. A combination of immediate military factors as well as political paralysis at the upper echelons of the French state prevented this from occurring.
The French situation in late May 1940 was quite grave for France. The German offensive in the Low Countries and Ardennes had broken through to the Channel. France had lost a good deal of its best military equipment and front-line troops in these battles, making the possibility of the French holding the line at the Somme defensive line quite difficult. But as the Germans prepared for Fall Rot, the invasion of French proper, there were small signs for optimism. French troops on the front had fought hard in the earlier stages of the conflict and there were signs that morale and performance was stiffening despite the defeats. While the loss of French equipment was dire, the Germans too had lost their own fair share of men and material in their lighting advance. While the opening phases of Rot would show that optimism was misplaced, there was a last ditch hope that a second miracle of the Marne would occur.
Such hopes though only made the confusion within the French leadership even more muddled. The scale of the initial defeats deeply shocked the French establishment and instead of forcing French elites to work together, defeat only exacerbated political infighting. Conservative PM Paul Reynaud had staked great hopes on standing and fighting the invasion, but the military men he had brought in to resolve this problem, Weygaund and Petain, beleived that resistance was futile and an armistice was the best option. Thus the French military leadership spent these agonizing weeks in May fighting their own political battles rather than the real problems of French command and control that was one of the reasons for the earlier defeats. Reynaud also found himself under attack by his Deputy Premier, Paul Baudouin, an Action Française ideologue who used the panic to attack the left-wing and other Popular Front veterans within the government. Reynaud himself was not above blame for this fratricidal politics, as his relationship with Daladier was toxic and characterized by mutual antipathy.
Paralysis at the top of the French government meant that defeat with the impending German invasion, already quite high, became a near certainty. Action Française-types and other archconservative and reactionary types began to argue that an armistice was the only real way to preserve French power and this wing of the French right was in clear ascendancy by June. By this time, neither the Breton plan nor a mass evacuation to North Africa were really possible. There was some talk of replicating either the recent Dutch or Belgian examples, where the French government left the country to form a government in exile. When Reynaud broached the possibility of such an option on 15 Hune, Weygaund flat-out told the PM that France would simply replace the executive. The knives of the the various rightists were out at this point and the ascendant right would castigate any appearance of exile as desertion, not continuing the fight. Reynaud's resignation of 16 June was a tacit recognition that had he formed an exile government, Weygand and Petain would simply form a new one in his absence.
An armistice evolved out of the French right's taking over inside this political vacuum. As the military situation worsened, there were fewer alternatives to preserving French power. Neither the British nor the French military leadership was confident that a Breton redoubt or North African evacuation would be feasible. Italy's entry into the war on 10 June signified that not even North Africa was a safe refuge as both Libya and possibly Spanish Morocco could eviscerate any regrouping of French power. The continuing German advance also put in danger the last reserves of French manpower and material in the south. For many on the French right, an accommodation with Germany would allow them to preserve French sovereignty and kernels of French power. Hitler, contrary to expectations, was willing to cut France some initial slack in these initial armistice negotiations over the French colonies, that status of PoWs, and the French military. Gambling all on a patriotic defense was unlikely, and would be embarrassing if France were carved up not only by Germany, but two jackals like Franco and Mussolini.
The ease with which the French government slipped from resistance to collaboration was itself a sign of the fascist leanings of the French right. The Vichy state simultaneously sought to restore French power, restructure the state, and exact political revenge on its left and center opponents of the 1930s. Not surprisingly, Vichy failed at all three due not only to German occupation demands, but also the fractious nature of the French right. For all the haranguing of the Popular Front by Action Française ideologues like Maurras, Vichy more closely resembled the AF's strawman of the Third Republic. from an organic polity based on tradition and hierarchy, the Vichy state was the antithesis of Maurras's vision. It was highly technocratic and its economic centralization of the economy did little for the French peasantry valorized by Action Française. Rather than promoting regionalism and a limited corporatist state, the Vichy regime cut down on regional autonomy. That Maurras and few other reactionaries seldom attacked Vichy on these grounds but actually pushed many of these developments illustrates the hollowness of much French reactionary thought of the 1930s.
These political divisions stand in stark contrast to other responses to German invasion, especially the Soviet. Although the popular image of the Purges has contributed to the notion that the Stalinist state was characterized my endemic suspicion and betrayal, the situation was rather more complicated. While the Purges did wreak havoc among the military and mid-level bureaucracy, there existed within Stalin's inner circle a cadre of hard-nosed bureaucrats and servitors. Termed "Team Stalin" by historians like Steven Wheatcroft and Sheila Fitzpatrick, this group emerged from the Purges largely unscathed. Likewise, the 5YPs did create a cadre of bureaucrats and other experienced individuals whose ranks were thinned out by the Terror, but still remained. Thus, in contrast to the French, the Soviet leadership did not turn on each other after Barbarossa. Counter-intuitively, Stalin actually eased up on the reins of power and let a number of these regional administrators do their jobs. The 5YPs and the Purges had actually prepared them to work under a crisis environment, only this time it was not of the state's own making. Additionally, the internal paranoia of the Stalinist state also helped the Soviet recovery. Although both wartime and postwar mythology enshrined images of factories removed wholesale into the Urals, the reality was that evacuation only saved approximately 13% of Soviet pre-war industrial assets. Instead, Soviet heavy industry was always primed for a massive expansion if needed. The Soviet defense industry had built-in factors to allow for rapid expansion. Factories built under the FYP typically had excess machinery and the mass mobilization of the prewar period habituated Soviet workers and managers to methods of mass production.
So in addition to having greater time to respond to the German invasion as well as far more space, the Soviet leadership on all levels was far more united than the French example from the previous year. French politicians like Reynaud simply did not have the political capital to pursue a resistance strategy after the May defeats. The chances of a successful resistance were already quite slim because of the situation on the ground and would have needed a unity not present in the French political world. An armistice soon emerged as the path of least resistance for the emerging Vichy leadership, so not surprisingly, they took it. Only relative outsiders like De Gaulle could afford to push for a resistance at all costs.
Sources
Blatt, Joel. The French Defeat of 1940: Reassessments. Providence: Berghahn Books, 1998.
Nord, Philip G. France 1940: Defending the Republic. New Haven: Yale University Press, 2015.
Paxton, Robert Owen. Vichy France: Old Guard and New Order 1940-1944. New York: Columbia Univ. Press, 2001.
_. The Fall of France: The Nazi Invasion of 1940. Oxford [u.a.]: Oxford Univ. Press, 2004.