The opera was written for the newly(ish)-rebuilt San Carlo, so a bit of spectacle would have been appropriate. The ballet was definitely written for Naples, not Paris, and it's the only ballet music that I'm aware of that Rossini included in any of his operas before he moved to Paris (Guillaume Tell certainly had a ballet, so did his French revision of MosŤ - which recycled some of the Armida ballet - and I'm fairly sure there's some dancing in Il Viaggio a Reims.)
I can't find any evidence that Armida was performed in Paris, though an opera called Robert Bruce (a pasticcio, with music culled from various Rossini operas including Armida) was premiered there at the end of 1846.
Another oddity is that Rossini wasn't in favour of supernatural elements in opera - hence Cenerentola had no fairy godmother - but that isn't apparent in Armida, with demons and allegorical figures and what-have-you. Lots of composers, notably Handel, Haydn, Salieri, Lully and Gluck, had already written Armida operas, however, and the well-known story probably meant that Rossini was unable to avoid magic on this occasion.Incidentally, it was one of three operas that he wrote within ten months.
One of my books says that Armida wasn't much appreciated at the time, but that it was a big stepping-stone towards his later operas.