Actuellement en licence de gestion à l'université X je souhaite vivement participer au programme Erasmus et ainsi acquérir une expérience de qualité.
Currently studying at Machin university as a third year student, I would really like to participate in the Erasmus prgramm and gain an experience of quality (sic).
Mais ça serait mieux :
Currently studying at Machin university as a third year student, I am deeply interested in taking part in the Erasmus program that is the opportunity to live a very interesting/an amazing experience in a foreign country.
Le Master X que vous proposez ayant pour objectif de former des professionnels gestionnaires, rentrerait en totale adéquation avec ma volonté d'intégrer un cabinet d'audit
As the master X offered by your university aim at training managers, it would perfectly fit with my volonty to enter an auditing firm when I could tick some numbers all day long.
