English is relatively unique in emphasizing the present progressive over the simple present. Why the simple present should seem to mean that something happens regularly (“I eat meat”) and not right now is a good question for ELU or Linguistics. I’d be interested to learn how that developed.

French, on the other hand, follows the majority of European languages in using the simple present to mean that something is happening now.

That said, other Latinate languages do have a progressive that looks like English’s. Spanish:

Como sopa de pollo vs. Estoy comiendo sopa de pollo

(I’m eating chicken soup)

Italian:

Vengo vs. Sto venendo

(I’m coming)

So it is somewhat unexpected that the equivalent strategy is an ear-grating mistake in French:

Je viens vs. *Je suis venant

(I’m coming)

However, a language can always fall back on periphrasis to capture a meaning, and in this case the periphrasis is grammaticalized (it’s just a tense marker, not analyzed as separate words):

Je suis en train de venir.

What French has in common with the other Romance languages is that the explicit progressive is less common than the simple present, since the latter covers both meanings unless you want to strongly emphasize the progressive aspect.

Mais bien sûr qu’il existe ce “temps progressif du présent“

Pas besoin de périphrase pour l’exprimer et encore moins du très vilain en train de.

Le participe présent est très exactement fait pour cela.

Ton M. Lechat is cutting the hedge. se traduit très bien par M Lechat coupant sa haie.
Tu connais certainement la statue de Saint George tuant le dragon et non Saint George en train de tuer le dragon et tétrachiée de titres d’œuvres d’art à l’avenant.

Note que… C’est passant ici par hasard que je répond.

Unless there has been in the past traces of a trend soon vanished and related studies to be consulted, a question such as “Why aren’t there progressive tenses in French” can be left, I think, to the wonderings of a poet, would there be one to find the exercise interesting. It’s a little bit as asking “Why does water runs downwards?”; about all we can answer to that is that if there is a creator, well, he’s decided it to be so. What could it be that deprived that language of what is in the English language a staple means of expression? The French never thought of it, never could see this possibility as helpful? At the level of whimsicalities, a confirmed agent of change and creation in matters linguistic, there is again a good deal of speculation that might be made. Would you search for answers in the realm of the logic associated with language? Surely not, as no language is organised on the basis of an all encompassing logic; all the logic we can apply to language is applied in restricted domains and by using only the rudiments of logic (most of all the logical constructions that has left us Lewis Carroll are useless except as curiosities and mental exercise), and the linguist has soon no use for all the complexity of logic. I do not think there is a reason that one could establish on sound enough logical grounds; as myriad questions of that sort we’re bound to dismiss that one as we do in reflecting about the particular position and shape of a knot in a piece of oak, it’s just there.

It should be added, as concerns the rest of the question that it contains the statement of a flagrant misconception. The time called “present” in English does not correspond to the usual french “présent”; in English there are three
variants of which the most important is called the “state present”; it’s the tense of actions that have no definite beginning and no definite end, just as the tense “imparfait” in French, except that the span of the action encompasses past and present; “Mr Lechat cuts the hedge.” is not equivalent to “Mr Lechat is cutting the hedge.”

Let’s make precise enough how that tense is used. One must understand that when the sentence is spoken the subject is almost never doing the action at the same time except by sheer coincidence; the tense expresses that the subject does habitually this action: he has done it in the past, he does it today and normally he’ll be doing it in times to come; there are various ways of saying that in French: “Tous les deux mois M. Lechat coupe sa haie.”, “M. Lechat a l’habitude de couper sa haie.”, “M. lechat et M. Souris se sont mis d’accord un jour l’année dernière: depuis M. Lechat coupe la haie et M. Souris coupe la pelouse.”

When the subject is doing the action at the time of speaking the state present must never be used; then, the progressive is used:

“M. Lechat is cutting the lawn.”

In French there are then two possibilities: M.Lechat est en train de couper sa haie.” (less common) et “M.Lechat coupe sa haie.” (common).