The original groups dropped off were a mix of Romans and Gauls scooped up indiscriminately from the middle of a clash between isolated units during Caesar’s conquest of Gaul. The Roman culture and organization was greatly superior, and the fact that the next group deposited was a cohort from the 2nd century Legio XV Apollinarius, scooped up along with native wives from what is today Uzbekistan reinforced the cultural dominance.
Byzantine line troopers and a handful of Hunnic mercenaries from Justinian’s expedition to Northern Africa that were believed lost at sea also were deposited in the same area, and as they were recognizably Roman and Latin-speaking, they were easily assimilated. The same could not be said for the Apache tribe deposited shortly thereafter, who remain a recognizable cultural minority to this day.
There were several more occasions where Byzantines of progressively later eras were deposited, then a gap of several hundred years, followed by the deposition of a group of Greeks of the 1919-1922 war with Turkey, cut off and surrounded by Turks, who remember only a bright light and awakening on a beach.
Politically, the structure of the Republic owes much to the Republic. Senators elect a pair of Consuls, who however remain Consul for Life. Unfortunately, the politics within the Senate are so vicious and violent that over ¾ of the Consuls die violently. Succession crises are fairly common.
Prior to the Great Central War, Swordpoint forces were a mix of heavy infantry units and cavalry in the Expeditionary Forces, questionable home defense forces, and a powerful Navy with ground forces of its own.