The French language belongs to the Romance language family, which is a group of languages that all evolved from the language of the Romans, Latin.
Each language in the Romance family has since evolved in different directions, and today they're all quite different from Latin.
Where did modern French come from?
Most of the language we call French today stem from the everyday Roman language "Vulgar Latin". It gradually changed and evolved into the Gallo-Romance language of the "Gaul" people whom we consider the main ancestors of the French today.
Celtic influences to the French language
Before the Romans arrived on the territory that we call France today, the people who already lived there spoke Celtic languages. Today, a few Celtic languages still exist. In North-Western France, Breton is still spoken today, and then there's Gaelige, the Irish language which is also Celtic.
A quite significant number of modern French words are supposed to having Celtic origins. Just to name a few, "alouette" (matchstick) "balai" (broom) "béret" (that stereotypical French head-dress!) and a ton of other words.
Frankish (Germanic) words in French
Similarly, modern French also borrowed quite a few words from the Franks who spoke a West-Germanic language closely related to English, Dutch and German.
The Frankish influence on French can be seen in words such as "guerre" (war) which comes from the Frankish "werra". The French "bourg" (small town) came from the Frankish word from "fortification". Then there are words such as "choisir" (to choose) which comes from the Frankish "kausjan" as well as quite a few others.
Modern English influencing modern French
Another Germanic language that's hugely influenced French, although much later, is English.
An English speaker learning French in our time might be surprised by the influence of English in the French language. The French even invent their own rules that somehow "look" like English and apply them to English verbs in order to turn them into French nouns.
An example of this is adding "-ing" to the end of an English verb. In English we'd assume that this is just the passive form of a verb.
But in French, adding the suffix "-ing" to certain English verbs turns them into nouns!
In modern French "un parking" is a parking lot, "un dressing" is a dressing-room. There are even older examples of this, like "un smoking" which is a tuxedo! (The kind of dress you wear when you go smoking, I suppose).
English words even influence modern French cuisine in creative ways. "Le snacking" has become a whole concept in French food, referring to small bite-sized dishes (but much fancier than fast-food!)
And then there are English words that become "fashionable" in French. I've lost count how many times I've seen the word "folklore" used in French. This can be quite amusing because it's a rare and quite specific word in English that sort of describes the cultural narrative of a group of people. In everyday French, the word is used much more liberally.
And then the rest of the world has left their marks too
Today, the French language is changing more than ever. France's colonial history has meant that the French people have made connections with peoples and cultures from all over the world, and those relationships (good or bad) are clearly visible today.
The North African "Derja" language (which is closely related to Arabic) continues to bring more and more loanwords into modern French. Most are considered slang, but slang-words tend to become official if people consistently keep using them.
It's not uncommon to hear French people ask for "un chouia" of something, meaning "a little bit" in Derja. Likewise, you'll currently hear the French exclaim "miskin" when they feel sorry for someone, and I recently saw a television show where an elderly (and unmistakably French) couple answered "inchallah" ("god willing" in Arabic) to a question posed by a journalist.
Finally: French is a Latin language, but..
So there's no doubt about the Latin origins of the French language. Yet, French hasn't been isolated since the fall of the Roman Empire, and has seen numerous influences from a lot of other languages.
Modern French is not just a natural evolution of Latin. It's a ragout of ingredients and spices from far and wide with Latin as the main ingredient.
And it's only getting more spicy!