Not sure what caused the 1990 spike, or the increase early in the century, ut while Fort Polk was technically established in 1941, closed around 1950, and reopened in 1961, it's its massive Vietnam-related expansion in the 60s that really transformed the Parish.
Louisiana increased by about 50% between 1890-1910. That particular area may have seen development of commercial lumbering, the same as west of the Sabine. Vernon Parish was not set off until 1880, and its growth from 1890 to 1900 was similar to 1900 to 1910 (and a much higher relative growth).
Beauregard, Allen, and Jefferson Davis to the south were not split off from Calacsieu until 1920.
The 1970 Census may have been the first to count military bases, I think that was when the Census Bureau started counting college students. Alternatively, Fort Polk had been closed down/mothballed after WWII (or just used as a NG base (many military bases in the South are named after Confederate generals because they were NG bases until WWI). The Polk in this cases is Leonidas rather than James K.
The 1970 was the first to delineate unincorporated areas of Fort Polk South and Fort Polk North. The police district with FP South increased in population from 1K to 19K between 1960 and 1970. The police district with FP North increased from 7K to 21K, but it includes Leesville, the county seat (which had about 9K).
From 1970 to 1980 FP North lost about 80% of its population, presumably due to a consolidation in the southern area. There was also some spreading out of the population in the county into more rural areas - perhaps civilians and ex-military acquiring acreages. The growth was also significant in the NW adjacent to Toledo Bend (the same has happened on the Texas side).