Not that I can think of, although the extensive Wikipedia article on the matter does mention the word "triad". That makes me think of an Asian criminal gang.
It seems unlikely to me that there is any widely-accepted equivalent term - "love triangle" is a very set and widely-used expression.
That said, there are many frequently-used terms that could also be used, but are less specific in their application. Examples off the top of my head include "romantic dramas", "twisted love stories" or "a juicy romantic theme".
Yes, don't let yourself be misled by Lis's French expression. That suggests that the three people involved are living together or at least have a 3-way consensual sexual relation with each other (perhaps even three-in-a-bed).
In a love triangle, as Grop points out, the relationships are not consensual. That is, (to use Grop's nomenclature) A is not usually happy that B loves C. In fact, A might not even know about it.