Hypercorrection
It can even influence a language: Fetus is the original Latin term, but it got "fixed" to foetus or fœtus both in how people wrote Latin, and also in languages that had a term derived from it so now foetus is sometimes found in English, Dutch and German and also fötus in German; all based on people "fixing" what wasn't broken.
In between personal hypercorrection and something introducing a new spelling that became common across four different languages, are myths like "the passive voice should be avoided", "don't start a sentence with a conjunction", "don't start a sentence with however", "don't split infinitives", "don't split any verb form", "don't end a sentence with a preposition", "don't use the genitive of an noun that represents a non-living thing", "don't use like as a conjunctive". Here not only has someone got a bizarre notion into their heads about what is correct, but the "rule" has ended up being actively taught.
Often it's combined with an incorrect understanding of its own terms, as in this notorious example:
source
Not only is this teacher enforcing an imaginary rule, but of the 10 cases marked as "P.V.", only three are in the passive voice. Of those 3, only one seems like it could be rewritten into something that didn't weaken it (and that one still wouldn't actually improve). One actual use of the passive voice isn't marked as such.
In theory, such a "rule" could become so popular, that it became a real rule just by dominating the thinking of those who spoke the language. Many though are actually impossible to follow consistently, or just too at odds with common literate use, to ever reach that point.
Plain as day ( can also be used with the physical reference you are hinting at):
also, plain as the nose on your face :
to be very obvious.
- There's no doubt that he's interested in her. It's as plain as the nose on your face.
(from www.dictionary.reference.com)
Best Answer
Yes, there's the same term in English, "broken English". First of all, there's a massive difference between having an accent and speaking poor English. You can have an accent and be very good at speaking a language. Think of former US Secretary of State Henry Kissinger, who always kept his heavy German accent, but was a diplomat and negotiator, both things that require you to have good command of the language you use. There are many people like this. You can describe an accent as "heavy" or "strong" if it's pronounced. Otherwise you can say a "mild" or "slight" accent. People who speak with even the heaviest accents, even to the point of being incomprehensible to an individual, may speak excellently; this would not be broken English.
Broken English Wikipedia article
Some definitions mention speaking slowly, or speaking with gaps, or making mistakes. However the term could generally be taken simply to mean that you don't speak the language well. In other words although the "broken" in "broken English" may suggest the "breaking/separating" of sentences with gaps due to difficulty in finding the right words, this is not purely essential. It may just mean you make a lot of errors. Also note that "broken" can be used for other languages. You can see the example above of "broken French", though this is less common.
I noticed your question in a comment:
Broken English isn't a language in the same way as French, Arabic or even Sicilian (which is called a dialect in many cases). But if we look at some definitions of language we see that it actually might make sense:
The first example, "your language is disgusting", is obviously not referring to a language such as French or English, but the manner of speaking or certain words used.
In the second two examples we have "form or manner", or "style", for example "the beauty of Shakespeare's language" and "Shakespearean language".
The phrase "the beauty of Shakespeare's language" is not referring to Early Modern English or Elizabethan English, it's referring to the style of Shakespeare's language.
In light of these meanings I don't see the problem with saying what you want to say. It would probably be taken humorously, because broken English isn't a language in the way most people understand it, that is, like French. If you feel comfortable being facetious and irreverent, that's totally fine to say. It's quite funny. However if you're writing seriously, maybe for a school paper, you should probably avoid it and rephrase it.