There are all kinds of reasons to learn a foreign language in general, and French in particular. Let's start with the general.
Why learn a foreign language?
An obvious reason to learn a new language is to be able to communicate with the people who speak it. This includes both the people you meet when traveling as well as people in your own community. Your trip to another country will be greatly enhanced in both ease of communication and friendliness if you speak the language. Speaking another's language shows respect for that culture, and people in every country prefer it when tourists make an effort to speak the local language, even if all you can say in it is "hello" and "please." In addition, learning another language can also help you to communicate with local immigrant populations at home.
Speaking a new language helps you to get to know another people and culture, as language and culture go hand in hand. Because language simultaneously defines and is defined by the world around us, learning another language opens one's mind to new ideas and new ways of looking at the world.
For example, the fact that many languages have more than one translation of "you" indicates that these languages (and the cultures that speak them) place a greater emphasis on distinguishing between audiences than does English. French distinguishes between tu (familiar) and vous (formal/plural), while Spanish has five words that indicate one of four categories: familiar/singular (tú or vos, depending on the country), familiar/plural (vosotros), formal/singular (Ud.), and formal/plural (Uds.). Meanwhile, Arabic distinguishes between nta (masculine singular), nti (feminine singular), and ntuma (plural). In contrast, English uses "you" for masculine, feminine, familiar, formal, singular, and plural. The fact that these languages have such different ways of looking at "you" indicates cultural differences between the people who speak them: French and Spanish focus on familiarity vs formality, while Arabic emphasizes gender. This is just one example of many of the linguistic and cultural differences between languages.
In addition, when you speak another language, you can enjoy literature, film, and music in the original language. It is extremely difficult for a translation to be a perfect replica of the original; the best way to understand what the author really meant is to read what the author actually wrote.
Business and careers
Speaking more than one language is a skill which will increase your marketability. Schools and employers tend to prefer candidates who speak one or more foreign languages. Even though English is widely spoken in much of the world, the fact is that the global economy depends on communication. When dealing with France, for example, someone who speaks French will have an obvious advantage over someone who doesn't.
Learning another language can help you to understand your own. Many languages have contributed to the development of English, so learning those will teach you where words and even grammatical structures are from, and augment your vocabulary to boot. Also, in learning how another language differs from your own, you will increase your understanding of your own language. For many people, language is innate - we know how to say something, but we don't necessarily know why we say it that way. Learning another language can change that.
Each subsequent language you study will be, in some respects, a little easier, because you've already learned how to learn another language. Plus, if the languages are related, such as French and Spanish, German and Dutch, or Arabic and Hebrew, some of what you've already learned will apply to the new language as well, making the new language that much easier.
As years of foreign language study increase, math and verbal SAT scores increase. (1) Children who study a foreign language often have higher standardized test scores in math, reading, and language arts.
Foreign language study can help to increase problem-solving skills, memory, and self-discipline.
1) Admissions Testing Program of the College Board
Page 2 - Why learn French