Basically the thread title speaks for itself. What would be the world's lingua Franca without a European nation/s imposing one?
of course the America's is more or less a lost cause as far as preventing colonialism goes. But both India and the Middle East had the capacity to hold out against colonialism. India just required the Mughal's remaining strong in the North a
nd a couple of decades delay in the South as suggested by Flocculencio. As for the Middle East that merely requires the Ottomans to hold on, which they probably would have if not their close-run defeat by Russia in 1878*. It's not too unlikely for colonialism in Africa to be seriously lessened either- just have the French defeat the Prussian attempt to unite Germany* and you knock off France's desire to compensate for it's humiliation with African territory and a Germany that can join in, and without those Britain doesn't feel compelled to make advances to keep a share for themselves.
Europe would still have it's local lingua franca of French of course(more so in fact with a weaker Britain due to absence of colonies and no united Germany). The Islamic world has Arabic, not to mention Persian which held elevated position in India and the Ottoman realm(and of course Persia). And the East has Chinese.
But we can't completely rule out of the importance of English, since they're positioned for mercantile dominance even without fullblown conquest of India, and English settlement in America* should be positioned to do very well in any timeline just due to it's fundamental geography and demography(barring an earlier POD).
So without European force bringing one to dominance, which one of these 4(5?) would win out as the most prominent global language? And would their be any chance for voluntary standardization on a global level without one civilization forcefully imposing it on the others? I'm a little skeptical personally, since such things didn't happen even in local areas like Europe without conquest(ie. the spread of the Napoleonic, Soviet** and American** system) OTL.
*Yes I know these are all affected by butterflies. But you get the general idea.
**On that note, the whole dominance of European philosophy thing probably wouldn't happen either, since capitalism, communism, secularism, democratic republicanism and so on were European*** concepts that held little currency outside Europe before the imperial conquests. Be rather cool if fundamentally distinct philosophies might develop in the Middle East/uncolonized Africa/India... possibly even spreading to Europe and taking over in some cases

(albeit in a Europeanized form).
***On a further note, those weren't so much European as Anglo(communism excluded, and notwithstanding Roman and Greek pedigree of democratic and republican ideas)- one wonders what continental Europe would look like with England and America to weak to anglicize their values.