I am aware that this question is rather more complex than I am treating it, but I am looking for a few general rules (e.g. basic phonotactic constraints) that would lead to the conclusion that the nonsense word "frabjous" conforms to English phonotactics. Any help (even if it is only a cursory explanation) would be much appreciated.
You mention the pronunciation
/ˈfɹæb.dʒəs/ in the comments; this is how I would pronounce it too.
Phonotactics are usually explained in terms of constraints ("you can't do this"), so the short answer is that it doesn't violate any of those constraints.
If we look at all the parts individually:
/fɹ/is a valid onset, as in "frog"
/æb/is a valid rime, as in "lab"
/dʒ/is a valid onset, as in "job"
/əs/is a valid rime (in an unstressed syllable), as in "ruinous"
- a stressed closed syllable followed by an unstressed closed syllable is a valid stress pattern, as in "madness"
And for the most part, any onset can be combined with any rime in English. So if all the onsets and rimes are valid, and the stress pattern is valid, the word is generally valid.
As a new contributor myself, I have to post this as an answer, though it's slight enough that it should really be a comment on Draconis' excellent answer (specifically a response to TKR's comment on it).
I think the spelling makes <frabjous> look a bit less English than it sounds. Draconis enumerates lots of good reasons for why it's phonotactically English, but to my mind, the spelling <-jous> seems a bit odd. However, the Latinate suffix <-dious> (<tedious>, <studious>), while normally pronounced /diəs/, is generally unstressed, so, in many dialects it can be reduced to something approximating [dʒəs]. And to my eyes, <frabdious> looks a bit less alien (it would look even less weird as <frabjious> except that <-jious> seems not to occur anywhere).