Political words tend to change the meaning, but the original meaning of communism meant common ownership of all property. As such it was during all of the 19th century in practice equivalent to socialism and could be used more or less interchangeably.
Although the early usage of the word "Capitalism" meant having stock exchanges and investors, since the 19th century the word has acquired the more fundamental meaning of "private ownership of property".
In these senses of the word, capitalism vs communism is indeed a dichotomy, as something either is owned communally or not. Either everyone has a say over the usage of the property or not everyone has a say. (Although you can have both common ownership and private ownership at the same time, but of different things. As such hospitals may be owned by the state, but car factories not, for example).
In this viewpoint the left was definitely not stuck between a false dichotomy, as the dichotomy was true, and they had chosen one side of it.
However, the meaning of the word communism started changing after the Russian revolution. Socialism continued to mean common ownership, but Communism more and more meant a specific path to socialism, namely Marxism including it's bloody revolution and dictatorship of the proletariat.
As such, the dichotomy starts being false. Although the dichotomy between socialism and capitalism remains, communism then became just one form of socialism, with most notably reformist and democratic social democracy as a major option. But the "the left" was not caught in this false dichotomy, because social democrats tried that option. Only that part of the left (which got smaller and smaller every year) that still supported the communist dictatorships could be said to be confined in a false dichotomy. A confinement completely of their own choosing, of course.
After the fall of communism and the gradual realization that social democracy hasn't delivered, the word "communism" has again started to change meaning. "Social democracy" increasingly means what before would be called "social liberalism", capitalism with a strong protective state, "socialism" increasingly means "politicians being nice to people" and "communism" is starting to revert to its original meaning of "common ownership". As such, the dichotomy between communism and capitalism is again becoming a real one.
I would therefore say that:
No, the European left was not confined in a false dichotomy between capitalism and communism, unless you with "The European Left" means only those who supported or still support the communist dictatorships because they dislike capitalism. But that is a very narrow definition of "The European Left" (although undoubtedly some of this left was and is so sectarian that they wouldn't hesitate to agree with it).