I'm interested particularly in the 20th century and the second World War if that helps frame the answer - I know the cause was still somewhat relevant in the first decade or so of the 20th century, but were there other times a monarchy could have returned to France?
The consensus is that the monarchist really had their last chance in 1871.
At that Time the parlement was a monarchist majority and the countryside strongly support the Idea. But they didnt manage to convince the prétendant to the throne and by 1880 a Republican majority was achieve.
And by the 20th century monarchist in France was just a minor political power. The third Republic manage to implement itself and convince a lot of moderate monarchist to support the Republic.
Sécularism Law , industrialisation and the spread of syndicalist Idea make the countryside turn in favor of the left and gave up on monarchist Idea.
By 1940 the monarchist we're represent only by a minority of far rigth politician. And even if some support Vichy the project of bringing back the monarchy was never proposed