The French General Strike of May 1968 is a likely contender with around 10 million on strike out of a then population of about 51.2 million, or about 19.5% of the total population. This represented about two-thirds of the total workforce. Some sources put the number as high as 11 million (approx. 21.5% of the population).
L'Aurore was a French centre-right newspaper which included among its writers several members of the Académie française. This (weekend) edition is dated 25 & 26 May 1968 and has the sub-heading "mais 10 millions de Francais sont toujours en greve". Image source: cadeauretro.com
The figure of 10 million is the most widely given, and was quoted by publications at both ends of the political spectrum. The article General Strike: France 1968 - A factory by factory account gives figures which show how the numbers increased during May 1968:
From a few hundred strikers on 14th May at the Sud-Aviation air craft
factory in Nantes the strike spread rapidly: 2 million strikers by
18th May, 9 million by 24th May, reaching nearly 10 million two days
The Historical Dictionary of France also gives 9 million for 24th May, but doesn't give a number after that.
A Journal of Labor Economics (Univ. of Chicago, 2008) article, Vive la Re´volution! Long-Term
Educational Returns of 1968 to the Angry Students (pdf) says
Over 10 million French workers were involved in the strikes—roughly
two-thirds of the French workforce.
This 2015 undergraduate thesis, “Peace Capital”: American Media 's Coverage of May 1968 in Paris (pdf) gives the highest number:
Over 11 million workers went on strike during May, which totaled over
20% of the population.
The figure of 11 million is also given by Wikipedia's May 1968 events in France.