If you’re familiar with the word café, le café is easy to memorize, especially if you’re just starting to learn. La rue is not as easy. It could look like the English table you already know, but you still need to know the article. Here is where noun gender starts confusing people. Just knowing the word is not enough in French. Usually nouns have articles attached, which can influence the rest of the sentence.
I recommend thinking of le, la, un, une as part of the vocabulary itself, not additional grammar. Don’t just learn the word café, rue, table, livre; learn le café, la rue, une table, un livre. When you review the words, read aloud with the full phrase. This gives your mouth practice with the combination, which makes the article slightly easier to recall. This way you’ll also be better prepared to make a simple sentence, since people rarely use isolated nouns during conversation in French.
The issue is not only that the articles can be difficult to remember. Noun gender can affect how other words in a sentence are pronounced or spelled. If you memorize phrases such as un petit café and une petite table, you learn how adjectives must change to agree with the noun. Because the word table is feminine, you must say the adjective petite and not petit. People who just learn the words without articles may understand the meaning of the noun when they encounter it, but then be confused or frustrated when they try to write a complete sentence. Articles can give you a good clue about what changes will be made later in the sentence.
One thing to try is to focus on a single topic or theme and memorize the six to eight most common French nouns related to that theme. Learn the articles and a complete noun phrase: le menu, la table, un café, une eau, l’addition, le prix. Read the noun phrases aloud, and then hide the articles and try to remember what went before each word. Try putting two or three of the phrases into a complete sentence: Je voudrais un café, Le prix est ici. The more you limit yourself to one topic for your noun phrase vocabulary, the more efficient it will be, instead of learning random disconnected words.
Auditory practice can help you learn articles for nouns, too. When you listen to slow, learner-level audio, try to listen for the articles. Le and la are very short words, but they carry important information. Un and une are different sounds and these are important to memorize, too, when you try to repeat a sentence. If you only listen for the content word of the noun phrase, you’ll often completely miss the articles. Try to isolate the noun phrase and repeat that only (instead of the whole sentence) if it feels like it’s hard to learn a whole sentence at once.
It’s normal for many nouns to just seem arbitrary. It’s impossible to use logic to guess which words are masculine or feminine, even for people who already speak French fluently. The goal is simply to slowly build your vocabulary of useful French phrases. Whenever you learn a new vocabulary word, remember that you need to know the noun article before you move on. It will be easier to memorize other articles later in your course if you start practicing this as soon as possible. Otherwise, it’s very difficult to add an article to a noun if you already stored the word without the article in the first place.