Yes it does.
I am eating = je suis en train de manger = tá mé ag ithe.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

"en train de" sounds like more of a phrase than a tense.

Okay, so let me rephrase my answer: French doesn't have a progressive construction that is as close as the parallel constructions existing in Celtic languages and English. (Is the Icelandic one also parallel to the Celtic-English one?)

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

because the preposition has 3 words in French vs 1 in Irish?
But you could say "tá mé ag ithe" isn't a tense either when compared to English, (which doesn't use a preposition), or even that even in English it's not a tense when compared to Basque ((ba)noa = I'm going, in 1 word ).
What's the border between "tense" and "tense expressed by a phrase"? After all, "tá mé ag ithe" is a phrase too...

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

We are looking at the degree of parallelness of the constructions. The use of a "be" verb and a verbal noun is very close and it is sometimes assumed that the Celtic languages adopted the construction from English, but since continental Germanic languages don't have the construction, it is possible the influence was the other way around.

There are other constructions in Irish that likely entered Irish from French under the influence of the Normans and possibly earlier ones still from the Latin of the Bible.

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

An Bhriotáinis fosta?

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Céard é an dul cainte comhionann sa Bhriotáinis?

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Tá mé ag ithe = (é) h-oun (é) tébein (in mo chanúint).

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne