All the Romance Languages that exist in real life are descended from the colloquial Latin of the later Western Empire, generally known as Vulgar Latin. This constrained what could evolve, and gave rise to the common features of its descendents. However, it seems possible that had something branched off from Latin at a different point in its history, a very different sort of Romance Language might have evolved. Here are some things that might have happened otherwise.
- Word final <m> in Classical Latin seems to have been pronounced as a nasalization of the preceeding vowel. Vowels at the end of words seem to have been elided when the next word began with a vowel (as far as we can tell from poetry), and this includes the nasalized ones. Latin's basic word order was SOV, and singular accusatives ended with an <m>. This could lead to the situation where the object is incorporated into the verb.
- As a further consequence of this, the accusative (minus its original ending) becomes the main form of the noun, and we have a marked nominative system.
- /h/ was lost in Vulgar Latin - by the fourth century AD, only lawyers and politicians pronounced it, and they needed special training. However, in the first century BC, we have evidence that people "on the up" tended to overproduce it. So words beginning with vowels in Latin begin with /h/ in this language.
- As a result of this, voiceless stops become a bit aspirated, except in clusters, like they do in English. People learning the language tended to get voiceless stops following an /s/ mixed up with voiced stops, so we have the sound change /sp st sk/ => /b d g/
- However, for stops that were already followed by /h/ become affricates. So the word spatha (sword) becomes bats.
- The ending -que (meaning "and" SENATUS POPULUSQUE ROMANUS) is still around, and doesn't get lost as it did in Vulgar Latin.
Obviously, this needs a backstory. My idea is that during the Second Triumvirate, a Roman merchant ship returning to Egypt from India got blown off course in a storm and was wrecked somewhere in what's now southern Somalia. Unable to repair their vessel, the crew traded their cargo of luxury goods for the things they needed to set up a colony (including women).