By "false" concept, I presume you mean an "invalid" or malformed concept. Propositions are true or false. Concepts are valid or invalid.
An invalid concept is one which denotes a grouping of existents that cannot be considered as a group for purposes of rational thinking. For instance, a concept "roundoid" meaning "any round thing" isn't valid because the roundness of a thing is, in most contexts, not an essential attribute (though "roundoid" might be a valid concept in the context of a game which contains only round and square pieces. But then the definition of "roundoid" would be more specific: "a round playing piece in the game of Rou-Squa(TM) ).
Invalid concepts generally package things which are not essentially similar into a single group. For example, "extremism", which invalidly packages extremely irrational thinking with extremely rational thinking.
A less common form of invalid concept is one which arbitrarily separates some things from other things: for instance a concept like "gwapple" which might denote "green apples currently owned by women". There's just no good reason to form this concept.
A false dichotomy is a claim that there are only two possibilities in a particular context, when in fact there is at least one other possibility.
For example: "You can be more like a Republican, or more like a Democrat." Here, it is claimed, there are only two political directions. Looking closer, we see that this alternative can be analyzed. One side represents greater material freedom at the expense of spiritual freedom, and the other represents greater spiritual freedom at the expense of material freedom.
This false dichotomy stems from a premise that freedom is a zero-sum game between the spiritual and the material -- that you can't have both spiritual and material freedom. Once that premise is identified and refuted (no easy task), a third alternative emerges: one of both spiritual and material freedom, which has been, due to a mistaken premise, outside the imagination of most people.
An invalid concept can cause a false dichotomy, but a false dichotomy can't cause an invalid concept. This is because concepts are fundamental to propositions.
In fact, one might plausibly (though mistakenly) argue that "Republican" and "Democrat" are invalid concepts because each represents a packaging of a form of slavery with a form of freedom. Still, these concepts are valid, because people who accept these exact contradictions actually exist.