Well let's do some math. On average it's about a billion per plant. To actually replace coal and gas as well as reduce carbon emissions, it's somewhere around a thousand nuclear plants. That's a trillion dollars.
Over what time period?
Where are you getting these numbers from?
France has 59 nuclear power plants which provide 425 TWh of electricity. Total consumption for the entire country was 451 TWh.
Because the US uses more electricity per capita than France, our total usage is 3,816 TWh. Thus, to power the entire country's electrical needs, we would need 545 plants.
Then, you have to consider the fact that the French plants are generally old and underpowered. The majority of them are 900 MWe plants, while the current generation of plants are 1650 MWe. Once you adjust for that, we would only need 297 of the new plants to cover our entire country's needs. Given that we already have 104, I don't think that this is so difficult to imagine implementing.
In terms of cost, you actually underestimated the expense associated with these plants. Estimates for each new plant in the US are $6-10 billion. If we take the middle figure of $8b and apply that to all 300 plants, that's $2.4T in total cost.
Now, the total cost of electricity in the US per year is $372b (9.78 cents/KWh * 3,816 TWh). That means that we would recoup the entire cost of all 300 nuclear plants in approximately 6.45 years.
That seems like a good investment to me.
(I know that I've ignored the costs of actually running the plants, but it appears to be relatively trivial compared to the costs of building/insuring the plants. If you like, tack on another $1b per plant and add a year or so to the total time.)
