You can use the present in both clauses:

Le jour où elle quitte Paris, Amélie veut vraiment maîtriser l’anglais.

The sentence is however not idiomatic. Vouloir doesn’t translate to want here. That should be something like:

Le jour où elle quitte Paris, Amélie doit vraiment maîtriser l’anglais.

or

Le jour où elle quitte Paris, il faut qu’Amélie maîtrise vraiment l’anglais.

Moreover, your reference sentence:

Le jour où elle quittera Paris, Amélie veut vraiment maîtriser l’anglais.

doesn’t work. That should be:

Le jour où elle quittera Paris, Amélie devra vraiment maîtriser l’anglais.

Note that in French, you certainly can use the present instead of the future without breaking hypothetical “cross-language generic logical rules”:

Demain, on rase gratis.

This sentence is not correct in any language on the count of logic, as the adverbial, whether “le jour où elle quitte Paris” or “le jour où elle quittera Paris” situates the action “vouloir” in the future. For instance, using actions of graded abstraction the impossibility is felt more clearly.

• Quand je serai en Chine je mange beaucoup de bon riz blanc. (Only “je mangerai”)
• Quand je serai en Chine je pense à un bon interprète. (Only “je penserai”)
• Quand je serai en Chine je veux un chapeau chinois. (Only “je voudrai” and even so a difficult prediction; one would rather say “Je crois que quand je serai en Chine je voudrai un chapeau chinois.”.)

You can replace “Quand je serai en Chine” by “Le jour où je serai en Chine” and even by “Le jour où je suis en Chine”, that makes no difference.

The action of “vouloir”, considered rationally, can’t be triggered by the action of going away; if the language has not been mastered there is no time left to justify a wish concerning a possible acquisition of mastery; there is a context only for regrets, or résolutions and wishes but not about the present inadequacy.

• Le jour où elle quittera Paris Amélie regrettera de n’avoir pas maitrisé l’anglais.

If the action of leaving has been planned, that of wanting to obtain a mastery of the English language is logically anterior to the time when leaving takes place and can’t be referred to as being associated with it. A different formulation is then needed, a formulation that rests on the basis of cause and effect relationship, more pertinent and realistic than the simple relashionship of mere coincidence in time.

• En prévision du jour où elle quitte/quittera Paris, Amélie veut maitriser l’anglais.

A slight modification makes of the adverbial of time (when the action takes place) an adverbial of cause (What for ? So as to do what is necessary for a given happening).

Of course, one can choose the time in the future as a simple limit that Amélie imposes upon herself and one understands implicitly that the mastery of English is aimed at making her sojourn in foreign lands more profitable. However, another construction is needed.

• Amélie veut vraiment avoir maîtrisé l’anglais avant le jour où elle quittera Paris.

I’m not sure whether this is grammatical or not (the answer from jlliagre seems to indicate it is) but I (native – Belgium) understand the meaning of the sentence as it would be understood in your language I guess.

I can think of several examples I find idiomatic using the same pattern:

Le jour où je suis riche, je m’achète un penthouse à New-York.

Le jour ou j’ai des enfants, j’arrête de fumer.

Le jour où tu me rembourses toutes tes dettes, je te reparle volontiers.

That said, to convey the same meaning using the same words and look more idiomatic, I would rather say

Emilie veut maîtriser l’anglais pour le jour où elle quitte Paris

or

Emilie veut maîtriser l’anglais avant de quitter Paris

This should remove the misunderstanding that comes with your initial formulation that you can witness in the other answers