Ruzain is the diminutive form of Razeen, the same way Husain is the diminutive form of Hasan. Razeen has a good meaning ("calm", "composed", "well-balanced") and is also the name of one of the Sahaba (Razeen bin Anas bin `Aamir), and Ruzain has the same meaning as Razeen. Since the meaning is good, Ruzain is an acceptable name for a Muslim child. The format of the name is usually used for boys (same as Husain and Umair), for this reason there is no issue with using it for a boy. The word Ruzain may be used often by people from French-Arabi cultures, but it is not from French-Arabic origins, it is a standard Arabic word from the R-Z-N root.
Muslims can use names from any origin as long as the names have a good meaning.
Aleesha might be another form of Alicia, which is an acceptable name: http://quranicnames.com/alicia/. The name may also be from other origins. If you'd like us to research the name further for you, let us know.
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