Up until World War II, French was the language of international communications. All diplomats would have to be conversant in French and in fact, even at the helight of the British Empire at Palmerston or Disraeli's times diplomats from the British Foreign Office used French rather than English to communicate with foreign representatives. Not many people learned English back then unless they were Dutch or Scandinavian, but almost every educated person knew French. English only became accepted usage in international affairs when the United States started to exert active influence in the world stage at the beginning of the 20th century - as the US State Department diplomats weren't too conversant in French.
In fact, although French has declined in international importance since 1945, it remains an important working language at this level. For example, in 1977 Italy and the then Yugoslavia signed a treaty finalizing the borders following post-World War II cedings and referenda. The treaty was written in French rather than English and any disputes regarding the treaty itself would be resolved according to the version in French.
Scientific and technical articles present an interesting angle. Germany was the leading power in this field up until 1945 and most American or British scientists (such as Millikan) would spend time in German universities for post-doctoral researches. Because of this plenty of scientific journal articles were first written in German and learning German was deemed necessary for most good scientists or engineers from the English-speaking world. Still, French was used as a working language to release many journal articles as well and thus many English-speaking scientists were often trilingual. Today, I think standards for measurements (SI units) are still drafted in French rather than English.
So learning French is a tool because it is still a working language for international communications while German is good if you want to delve into science and technology. But for most people knowing neither English nor French English would be the best language to master first.
I agree with your analysis. I studied German and Italian in college and picked up a other languages along the way. Learning Italian was more fun than Deutsch and helped me to read French and Spanish. Reading Hegel and Neitzche in German was daunting. In high school we had an exchange teacher come in for one year. We all acquired a Schwabisch accent. My professors were amazed when we recited in class because he claimed we sounded like natives.
English has 1 million words, whereas French has fewer than 100,000. In other words, English has 10 times the number of words than French. German only has 200,000 words, or 1/5 of the number in English. As a matter of fact, English has the biggest vocabulary of any other language on the earth. Perhaps that is why it is the most useful in so many different situations all over the globe. And, it is easier to learn one very useful language than many not-so-useful ones.