You are correct, the freesoilers faded about 2 years before the rise of the republicans. It was actually a pretty complex mess of a decade.
from Wiki
>>The party downplayed abolitionism and avoided the moral problems implicit in slavery. Members emphasized instead the threat slavery would pose to free white labor and northern businessmen in the new western territories. Although William Lloyd Garrison derided the party philosophy as “white manism,” the approach appealed to many moderate opponents of slavery. The 1848 platform pledged to promote limited internal improvements, work for a homestead law, paying off the public debt, and a moderate tariffs for revenue only.
The Compromise of 1850 temporarily neutralized the issue of slavery and undercut the party’s no-compromise position. Most Barnburners returned to the Democratic party, and the Free Soil Party became dominated by ardent anti-slavery leaders.
The party ran John P. Hale in the 1852 presidential election, but its share of the popular vote shrank to less than 5%. However, two years later, after enormous outrage over the Kansas-Nebraska Act of 1854, the remains of the Free Soil Party helped form the Republican Party.
Lincoln and VP Hamlin were elected as Republicans in 1860, but in 1864 Lincoln jettisoned Hamlin and ran with ‘War Democrat’ Johnson as ‘National Union’. Fremont, Republican candidate in 1856, ran as the Republican in 1864 until he realized the split vote would yield a ‘Peace Democrat’(McClellan) win.