a gap or breach

[alan gould]

un trou is a hole

la trouée i think is a gap or breach

the dictionary says la breche is a breach or gap.  it says it's used figuratively to mean "to make a dent in sth" -- "ils ont ouvert une breche dans le monopole de l'opérateur historique".  in english u hear "to make a dent" usually regarding food or a task -- "i didn't finish it cuz there was so much, but at least i made a dent."  a dent is also btw when u slightly damage something like a car touches another car lightly in a parking lot.  there's no substantial damage, but the other car put a dent in the side of my car.  

[Chantal Savignat]

"Ils ont ouvert une brêche"

une brêche is very very small. imagine an big ice cube, you hit with a hammer, there is a kind of thin zigzag line with just a thin  opening : it's "une brêche" it's a fragility, if you hit in the same point, it will break ....

figuratively,

"ils ont ouvert une breche dans le monopole de l'opérateur historique"

it means that there was an existing big deal with one society and only this society, and no one could before do something against that with success. But then someone succeed to do something, maybe a very little thing but with success (it's the first shot on the ice)

[alan gould]

i'd say only an educated anglo uses it -- a breach in a wall, a breach in security, a breach in the audio.  gap is the common word.  

use "an" before a vowel and a "h" if it's not pronounced.  u want a smooth transition between vowel sounds.  so there's no reason to say "an big ice cube" but there's a reason to say "it was an honor to meet u."  the "h" isn't pronounced, but "honor" is spoken as if it's "onor" so u need "an" not "a."

"Ils ont ouvert une brêche"

une brêche is very very small. imagine an big ice cube, you hit with a hammer, there is a kind of thin zigzag line with just a thin  opening : it's "une brêche" it's a fragility, if you hit in the same point, it will break ....

figuratively,

"ils ont ouvert une breche dans le monopole de l'opérateur historique"

it means that there was an existing big deal with one society and only this society, and no one could before do something against that with success. But then someone succeed to do something, maybe a very little thing but with success (it's the first shot on the ice)

i'm not sure what the above paragraph means but it's not important.  "and no one....

no one could successfully challenge it before or no one before could successfully challenge it.  i wouldn't put before after "could" but i don't think there's a reason.  it's just that it sounds better.  

succeed is used infrequently.  instead use "successful or" "successfully" 

u wrote "but then someone succeed to do something"  it would b someone succeeds but i'd write "manages to successfully challenge the system, the status quo."  i hope u manage or i hope u're successful.