I'm learning English, and want to learn Latin-based languages like French.

A note that "Latin-based" makes sense and people will understand what you mean, but the common term for these are "Romance languages"

For one reason, I want to know various values.

I'm not sure what you mean by "for one reason". I thought you might mean "for some reason" but this wouldn't fit the sentence very well since it implies you don't know the reason.
I am guessing you wanted to list reasons, so the common way to phrase this would be "For one, [put your reason here]".

I think languages represent how people who halive been living certain region recognizein different regions view the world.

Saying "a certain region" could give the impression you're talking about a single region.

Then, itus, learning those languages surely leads to understanding theire cultures deeply.

"Then" makes sense here, but "thus" feels a bit more natural to me. It indicates that what follows is a result of what came before it.
Changing to match cases etc with the previous sentence.

For one reason, I want to know various value systems.

"values" is a little too generic and ambiguous to sound natural here. "value systems" is a more formal term, but also more specific, so I think it sounds better here.

Alternatively, "I want to know what people in different parts of the world value" is an option too.

I think languages represent how people who have been living in certain regions recognize the world.

Then, itrefore, studying their language will surely lead to understanding theire culture deeply.

"Then" doesn't quite work here as the sentence is a bit too hypothetical for that, "Therefore" (formal) or "So" (casual) fit better here.

"there" -> noun for a unnamed place, like "over there".
"their" -> belonging to them

I'm learning English, and I want to learn Latin-based languages like French.

For oOne reason, I want to learn new languages is because I want to know about various values.

I think languages represent how people who have been living in certain region recognizes view the world.

"Recognize" isn't quite right here. To recognize something is to notice it and know it from before. "View" works better here.

Then, itis surely leads to understand ing othere cultures deeply.

I fixed this more generally to "other cultures". However, I think you meant "their cultures" , not "there cultures"
There = a place (e.g., that thing over there)
Their = possessive pronoun, belonging to someone (e.g., that's their dog)
They're = they + are (e.g., they're coming to the party today)
This is something that's confusing for some native English speakers!

Is that an exaggeration…?