His first publications, which appeared anonymously in local journals, were also classical, consisting of metrical translations from the Greek anthology.
Falconer is perhaps best known in the present day for his works on the Bostan, from which he published in 1839 a volume of selections, very neatly lithographed from his own transcript.
In the Asiatic Journal, a useful periodical now defunct, he published a translation of part of the same poem, as well as selections from several of the Sufi poets, and a critical study of the Sindbad-Nameh.
Falconer edited two important poems of Jāmi, the Tuhfat-ul-Ahrār and Salāmān u Absāl, for the Society for the Publication of Oriental Texts.
The critical ability of these texts is attested by Francis Johnson in the preface to his edition of John Richardson's Persian Dictionary.