Learn French: Le médicament a fait de l'effet.

They use the same base noun, but mean entirely different things. En effet is a fixed phrase meaning 'indeed' or 'actually'. In this sentence, de l'effet is simply the noun effet (effect) combined with the partitive article de l' (some). The phrase faire de l'effet means 'to have an effect' or 'to take effect'.

Why do we use a fait here when the English translation says 'took'?

In English, a medicine 'takes' effect, but French uses the verb faire (to do / to make). Literally, the medicine 'made some effect'. This is a set expression you simply have to memorize: faire de l'effet.

Why do we need de l' before effet instead of just un effet or l'effet?

De l' is the partitive article meaning 'some'. French uses it here because the medicine produced an unspecified amount of effect. If you used the definite article l'effet (the effect), you would have to explain exactly which specific effect you mean.

I always mix up médicament and médecine. What is the difference?