So, a return to a monarchy was a real possibility in 1871, but the reasons why it didnt happen go far beyond flags.

First off, public opinion was not as pro-monarchist as you think. Its very important that the election of 1871 was held only in the parts of France that the Thiers regime actually held (ie, not the capital). Even after the 'Rural Assembly' of 1871 had finished its bloody business of machine-gunning or deporting any Communards they found, that still left quite a few Parisians who, while not socialists or revolutionaries, certainly didn't want a return to the monarchy. A myth developed among socialist exiles that the Commune, while defeated, had 'saved the Republic' through its resistance; I absolutely don't buy that explanation, but it does give some impression of the strength of feeling, especially in Paris, of anti-monarchist feeling. Even outside of Paris, away from the fight between Communards and right-wingers, there was a very influential third faction of moderate Republicans (like Gambetta) who condemned the Commune but were also strongly anticlerical and anti-monarchist. It was this third group that would remake France in their own image and consolidate the Republic, not the conservative-liberal Assembly of 1871 that crushed the Commune.

There's also the thorny question of who the king should be. While the Orleanists and Legitimists managed to compromise on Henri de Bourbon as a candidate, the splits of the previous decades were still visible. The rival claim of the Bonapartists, who offered Napoleon IV (before he was stabbed repeatedly by a Zulu war party in South Africa in 1879), further complicated matters. The consensus, from what I've read, seems to be that the republic was on very shaky footing until about 1877ish; at that point, public opinion had turned against the monarchists and MacMahon's attempt to fix the election was drowned out by public support for the republic, which began to assert itself more self-confidently.

My own personal take is that the Republic survived by defining itself against the Paris Commune. The chaos of 1871 produced a crisis of authority that could have gone in any number of different directions, but it was the demonisation and repression of the left that allowed the new Third Republic to appeal to conservative-minded Frenchmen as, if not ideal, certainly an acceptable form of government. The legacy of the Commune was the association of the Republic with upholding Order and Property (not threatening it, as previous Republics were accused) and made possible a compromise between monarchists and liberals. So maybe Prosper-Olivier Lissagaray (Communard and Marx's son-in-law) was right, and the Commune did save the Republic. I'm not sure he'd like that interpretation though....

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If you're interested, the best books about the early Third Republic and the Commune are Collette Wilson's The Politics of Forgetting, Robert Tombs' The War Against Paris and th relevant chapters of Maurice Agulhon's Marianne Into Battle: Republican Imagery and Symbolism in France 1789-1880