"Sector" as an English translation for "secteur" is actually a bit of a false friend translation in this example. "Sector" in English in an economic context generally refers to a very large division of the economy - the private sector, for instance. The standard way to refer to fishing as an economic activity that is part of the economy is "the fishing industry." Here is a sentence taken from an English-language source (not translated), for instance: "The fishing industry includes any industry or activity concerned with taking, culturing, processing, preserving, storing, transporting, marketing or selling fish or fish products." And here is a recent headline from the New York Times: "Hawaii Lawmakers Press Fishing Industry." The preferred translation should definitely by "Fishing is an important industry" because that is the most natural way to express this idea in English. Just to be clear, I'm not suggesting that "sector" should necessarily be marked wrong, but rather that "industry" should be the preferred translation.
I would more commonly call fishing an industry in this context rather than a 'sector' (Australian English). Perhaps sector is an American term?
Nope. I'm an American English professor, and I came to the discussion to figure out what this sentence even means. "Industry" would be a much better translation.
I think "sector" would only be used one you had established that you were talking about industry. Without that prior context, "industry" is much better.
in this context in canada we would say the fishery is an important sector because as a sector it is not so much an activity (like fishing) as an economic area, (sector)
"...an important industry" makes a lot of sense but the word for "industry" (l'industrie) is not part of Duo's vocabulary. So someone thought that "secteur" would have to do. One could use this expression to refer to an economic segment of a country, thus, secteur agricole/bancaire/hospitalier = farming/banking/hospital sector. In everyday language, "le secteur de la pêche" would be called "the fishing industry" or alternatively, "the fishing/fisheries sector". Similarly, in this context, it could be understood as "Fishing is an important industry".