The whole notion of an "old" language is linguistically nonsensical. All natural languages, save for creole languages, trace their roots further back into history than we can look. Some are more conservative than others (I. E. they have changed less - but all languages change), but they're all the same age: older than recorded history.
Is French older than recorded history? No, Latin, Vulgar Latin, Gallo-Romance from before the 8th century are different languages and cannot be called French.
Similarly, all life on Earth is part of a single phylogenetic tree, but it does not mean that all species are equally old: Homo sapiens diverged from earlier hominids about 300 thousand years ago, and Canis lupus (gray wolf) diverged from its ancestors about 1.1 million years ago. Birds probably evolved from theropod dinosaurs.
You cannot say that all languages are the same age, just like you cannot say "Homo sapiens and hummingbirds are the same age: as old as life on Earth. They have changed over time, of course, for example 150 million years ago humans were small shrew-like mammals feeding on insects, and hummingbirds were large feathered dinosaurs, but all species change, the only difference being that some of them are more conservative than others".
The notion of an "old" language is like a notion of an "old" species. It is a language that has diverged from another language a lot of time ago, just like a species that diverges enough from its predecessors to get a new name.
You're missing the point. French does in fact trace its roots, i.e. its ancestry, to prehistory. The point is that it exists along a continuum with all its ancestral stages; there is no point at which "French" unambiguously pops into existence. The same is true for all natural languages; they evolve slowly over large timescales, and this rate tends to be similar over large enough time scales, as periods of greater and lesser rates of change average out. This same basic premise of more-or-less constant rates of change over large enough periods of time is how geneticists estimate dates of divergence. Obviously the rate is not completely constant.
More to the point, how would Finnish be considered an "old language", relative to other languages anyway? Assuming we're distinguishing it from Old Finnish, which (poorly attested) existed in the middle ages, Finnish is no older than modern English, French, Italian, German, Russian, Mandarin, Japanese or any other natural language. Even the common ancestor of all Finnic languages is relatively recent, 1500 or at most 2000 years old, comparable to Slavic or Western Romance.
As for those "earlier hominids" 300 kya, they are really the same species as H. sapiens; we haven't actually evolved much more quickly. Keep in mind that paleontological species names are based on morphology and convenience, not genetic distance. If we're being really strict, we and Neanderthals should be considered the same species, and the common ancestor between sapiens and them was more than 700 kya.
I find all this talk of important languages to be rather odd. Englis is important because it is becoming everyone's second language. Spanish is important because it is spoken by so very many people in this hemisphere. Chinese is because it is spoken in one form or another by a quarter of the people on the planet, but Chinese isn't a language but a family of languages, often not mutually intelligable. But much the same could be said of a language called Romance with vaious local or regional dialects, many of which are mutually unintelligable. The same might be said of English because my daughter in law [the wife of my son] moved from Australia to Texas where she couldn't understand anyone. So, you see, I cannot quite figure out what an important language is.