I like writeaway's suggestion in the Kudoz glossary - keep the French and add an explanation in brackets that is fairly universal, i.e. (secondary school diploma).

We don't know the country of origin of the source text and I'll just assume it's France - I couldn't speak about other French-speaking countries anyway, except perhaps to say that baccalauréat means "first (college) degree" (i.e. bachelor's degree) in Canada.

Anyway, I agree with previous answerers that it should be kept in French, followed by a universally-recognisable explanation.

While it is true that it happens at the end of secondary education, it is also, and perhaps more importantly, the first university degree in France:
"Le baccalauréat, premier grade universitaire. Créé en 1808, le baccalauréat est un diplôme du système éducatif français qui a la double particularité de sanctionner la fin des études secondaires et d'ouvrir l'accès à l'enseignement supérieur. Il constitue le premier grade universitaire." (https://www.education.gouv.fr/le-baccalaureat-premier-grade-... Of course, the exam has evolved over the years and nowadays prepares students for other things than a university education, but legally at least, it is still the first university degree here.

I don't know whether I'm the only person on this page actually to have sat this exam, but for your information, my (paper!) diploma confirms that le président du jury, enseignant à l'Université de Paris-IV has accepted that I passed. The document is signed, on behalf of the French Education Secretary, by the then Secrétaire d'État aux Universités.

Again, we don't know the context of your question, but the fact that this student has shown s-he was intellectually able to register for a college course is perhaps more important than confirming s-he "just" completed secondary education.

I chose "university entrance" as this is what I'm most familiar with (in the UK at least), but you also find "university admission". I'll leave specialist native speakers to decide which is best.

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Note added at 2 hrs (2021-05-26 16:04:19 GMT)
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Thank you for the additional information. So, France it is. I'll stick to my translation: I feel the "university entrance" angle is what matters here.