The language of the fifth century army, especially in the West, was Latin. Common soldiers would have communicated in Latin, even if some may not have spoken Latin as their mother tongue (unfortunately I am not a linguist, so I cannot discuss the presence of substrate languages like Gaulish or Brythonic amongst rural communities). The Latin of the army was a form of Vulgar Latin, and formed a unique demotic idiom, peppered with unique technical terminology, official nomenclature, and slang. This “sermo castrensis” (or “camp speech”) distinguished soldiers from other Latin speakers, and served to link soldiers drawn from different linguistic backgrounds. The unique language of the army thus fostered bonds between soldiers.

The Western officer class, as it was drawn from the provincial and imperial elite, was almost exclusively Latin speaking, although varying knowledge of Greek was certainly common. Men like Stilicho and Ricimer, being members of the Roman elite, would have spoken Latin. This fact is constantly overlooked- even if men like Stilicho and Ricimer were of Germanic descent, they were completely culturally Roman. As members of the elite classes, they participated fully in Greco-Roman elite culture- to do otherwise would have earned the scorn of their fellow elites. By labeling him as a “barbarian”, Stilicho’s enemies sought to de-legitimize him in the eyes of their fellow elites, for to act “barbarian”, and not Roman, was dishonorable. This is important when we consider that ideas of honor directly affected power relationships. It is also worth pointing out that many of the “barbarians” of Late Antiquity, such as Alaric or Theodoric the Great, were intimately familiar with Roman elite culture.

So to answer your question, men like Stilicho and Ricimer, as members of the Roman elite class, would have spoken Latin, because Latin (and to an extent, Greek) fluency was a vital component of Greco-Roman elite culture and conceptualizations of elite honor.