As you note, there is no future subjunctive tense in Latin - it was a purely Iberian development, which explains its absence from French, Italian, Romanian etc. It developed from the merger of two very similar Latin tenses:
188.8.131.52.4 The future subjunctive. As we saw in 184.108.40.206, the Latin of Spain saw the creation of a future subjunctive (and later a future perfect subjunctive), which had no equivalent in Classical Latin, but which developed from Latin paradigms with other values. These paradigms were the future perfect indicative (CANTAVERO) and the perfect subjunctive (CANTAVERIM). In both cases, as happened in the majority of the Latin perfective paradigms, the values expressed in Latin by these forms came to be expressed by new compound forms (respectively, HABERE HABEO CANTATUM and HABEAM CANTATUM, whence habre cantado and haya cantado) (see 220.127.116.11-3).
The paradigms CANTAVERO and CANTAVERIM, abbreviated to CANTARO and CANTARIM in the way examined in 18.104.22.168, differed morphologically only in the first person singular (-ARO vs. -ARIM), in the second person singular (-ARIS vs. -ARIS, a contrast eliminated by the regular development of final vowels), and in the accentuation of the first and second persons plural (-ÁRIMUS, -ÁRITIS vs. -ARÍMUS, -ARÍTIS, a difference which disappeared when speakers adopted the system of always stressing the theme vowel, here -ÁRIMUS, -ÁRITIS, in such cases; see 22.214.171.124.3). Consequently, the two paradigms were reduced to one in Old Spanish, with the occasional survival, in the first person singular, of -m (cantam), beside -re (cantare), or -r, if we take account of apocope of -e (see 126.96.36.199).