I don't know where you are from so you may or may not have this feature in your own language: Because French has noun genders (masculine and feminine), French schoolchildren learn all their nouns with the article, for example "le nez", "la bouche", so they always know what gender the word has. This is in contrast to English-speaking schoolchildren who just learn "nose", "mouth". It's just an idea that I thought of while reading your post but you could try to use this method for learning phrasal verbs.
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