That's also part of the reason why I picked it, although I've had a hard time finding the right data to support that hypothesis. It's not as easy as asking what the most commonly-spoken languages are; instead, you've got to ask which language to learn next gets you the largest increment of being able to talk to more folks. That means you've got to subtract out the folks that speak language X but also language Y that you already accounted for, so to do it properly the data set you start with has to tell you which set of languages each individual person in the world speaks.

(Also, it's almost certainly true that French is beaten out by Mandarin Chinese in terms of being the second language with the largest increment, but I picked French instead of Chinese to learn first because French speakers are distributed throughout the world, whereas most Chinese speakers are in China. And as you already noted for Spanish, it and Hindi lost out because even though they have more total speakers than French, the increment might not be as large because so many of them also speak English.)