It is an outcome of a complex of many causes that each appear to be minor, but together add up to an overwhelming advantage for English.

I'd even remove the "second language" qualification. Weighting speakers by power, it is easily the first language.

The following reasons, in order of importance are what created the situation. I'll assume as a baseline that only the other major colonial languages (Dutch, Spanish, Portuguese and French) were realistic candidates. Chinese is also interesting to consider in a counterfactual, and if China had been a real contender in the game of empires, I believe English would still have won out.

1. The openness of the language itself to local influences and heavy borrowing (unlike French, no purity concerns or authoritarian control)
2. The simplicity of the language (26 letter alphabet, no annoying gender things to memorize, no irritating accent marks, mostly phonetic pronunciation). This especially became a bigger factor once the typewriter became common, since English is easier to type than any other major language.
3. The non-aristocratic associations of the language (unlike French, Persian or Sanskrit). Besides a curious friendliness to certain kinds of poetry, English is a workmanlike, plain-speaking language. It does not particularly support rich and refined ornamentation in speaking and writing. It is harder to tell high, middle and low class people apart based purely on how they speak. For contrast, consider the rich vocabulary in French for high-culture cuisine (French seems to have a dozen culinary words for every English one).
4. The tendency of British colonialists to co-opt rather than radically displace local power structures, and especially their tendency to recruit locals into their administration at all but the highest levels (mainly a function of the small size of Britain with respect to the territories it conquered), which created an English-speaking middle class around the world (in India, this first happened in Bengal, resulting in the much-lampooned class of "babus"). The middle class, emerging as it does from the mobile, urban bourgeoisie (which most needs to communicate with linguistically foreign regions), dictates the second language in most cultures. England either created or co-opted the middle class in a lot of the world, starting with its own yeomanry.
5. The professionalization of science and technology in England during the Industrial Revolution, making it the language of choice for the first large-scale international discourses that went beyond diplomats and traders. Though France under Louis XIV/Colbert was quicker off the blocks, England's Royal Society developed into a more substantial institution. Industry and engineering being larger-scale activities than science, it also helped that the Industrial Revolution happened first in England.
6. Two major historically contingent causes: the lack of linguistic unity in India (compared to say, China) and the victory of the English over the Dutch in the English-Dutch wars (which led to English being the language of American colonization; France was never a real contender in the US, despite its huge on-paper claims prior to the Louisiana purchase). Together, the events made the worlds second most populous region (soon to be first) and its most powerful region (the US) English-driven. Numbers and power matter.

Overall, a mixed blessing. English is like Microsoft in some ways. The runners-up, French, is like the Mac: its primary weakness is its tendency towards doctrinal purity and elitism.