No, it appears to be you who, in your words, needs to learn your history. The Transcontinental Railroad ran from Omaha, NE to Sacramento, CA. The western portions were acquired from Mexico as a result of the Mexican War (Treaty of Guadalupe Hidalgo, 1848). The Central portions were acquired with the annexation of Texas (1845), which acquired it as a result of the Texas Revolution. Only the eastern portions would have been covered by the purchase of the French claims in the Louisiana Purchase. (Note, the French purported to transfer land which they did not actually hold, and which claims conflicted with the claims of the Texans.)
So perhaps 1/3 or less would have been over land purchased from France.
As to what was covered by the Florida Purchase (my guess as to what you were referring to as a purchase from Spain), the US gave up claims to territory in the west which France purported to have conveyed. (Yes, they did get rights to Oregon, but that was well out of the way of the railroad route.) But they didn't purchase any land later used for the Railroad. In fact, the land ceded to Spain was largely what was acquired from Texas in 1848.
The situation isn't analogous to the Alaska boondoggle at all. A more similar situation would be if the Feds would give a private developer small tracts of inacessable land in the Alaskan interior in exchange for building a road through the area. Perhaps the government could buy up the island in question at present values, and give 1% of the land to whoever would build the bridge at their own expense.
The routes from Sacramento to Oregon, and Sacramento all the way to New Orleans had the same land grants provided for by the Federal Government.
Along with 15 million dollars from the US Treasury.
Transcript of Treaty of Guadalupe Hidalgo (1848), see Article XII