Absolutely not, since it is a general statement, in English you do not need an article. The translated sentence, as far as I understand, should follow the standards of the target language.
But there's nothing technically wrong about "The emotions are important" and that is how you would say it in French. So both should be (and are) accepted.
It doesn't have to be a general statement. The context could, for example, be implying that the emotions of a particular film are important to appreciate the work.
Apparently whether in this case "Les émotions" should be translated a "emotions" or "the emotions". Both are accepted.
Quelle est la différence entre "les émotions" et "les sentiments" !? Ou bien ce sont des synonymes! ?
Both are what you feel. But émotion is for something you feel at a moment (angry, joy) and sentiment are more durable feelings (what you feel for others)
« Émotions » generally come as a reaction to something happening outside of you, whereas « sentiments » are coming from inside towards the outside world.
An easy way of remembering it is that the etymology of “emotion” is from “motion” (actually it is from Old French and eventually Latin, but you can still make the relation between the English words which both come from Latin), which implies that some “being” is “moved” (psychologically) by some external event, thus an immediate (one could actually say “instinctive”) psychological and physiological response (heart beat, adrenaline and other hormones, etc.) to an event. An emotion is thus generally short.
« sentiment », on the other hand, is related to “senses” (Latin sentio = perceive) and “mental” (Latin mentum = medium, in this case the senses being the medium between the outside world and the brain). So it is more about the cognitive and logical response to something that can be felt with the senses although we have mostly lost the “senses” part of it and kept the “mental” part of it, besides, it sometimes encompasses the subconscious as well, so the feeling might relate more to intuition than reason depending on the context. A feeling (« sentiment ») is generally long lasting (it is not an instant thing that goes away at once).
Pretty much as in English: "les emótions" translates as "emotions" and "les sentiments" translates as "feelings".
So the reason it is "importantes" and not "importants" is because émotion is feminine?
Why in multiple other exercises here is feeling the only possible translation allowed for émotion , but here feelings is not allowed as the translation for émotions ? Feelings and emotions are virtually synonymous in American English and this sentence seems to make sense using feelings so I am confused about when the translation of feeling is allowed for émotion and when it is not. Can someone help me? (I know the translation for sentiment is feeling as well, but that isn't helping me with my confusion with this word.)
You use the definite, not the indefinite, article when making a general statement about a group of things, viz. statements that are meant to refer to all the entities that make up that group.
I think "Feelings are important" is by far the better translation but DL taught me to fear that translation. We would almost never say "The emotions are important" but DL has taught us that we do say that.
Please read above posts explaining the clear difference between "sentiments" and "émotions".
Maybe a clearer translation to English would be be emotions =emotional feelings and sentiments = sentimental feelings?
Just think of this as what a violin teacher would say to a student who is tecnically gifted, but otherwise flat: "Come on! Show the emotions! The emotions are important!"
feelings are important is marked WRONG by this maddening, idiotic program
"Les émotions" and "les sentiments" are quite different notions in French (please read the above explanations). Even if you tend to use "emotions" and "feelings" interchangeably in English, please translate "les émotions" to "emotions" and "les sentiments" to "feelings". This will help you remember to distinguish them in French.