See earlier in the thread. The waste is highly radioactive, of course, and very hot for some time. First it is dumped in pools. If the pool floods or cracks, you end up with the Fukushima issue. Fortunately that went to the ocean primarily and so was diluted. But in the US, much of the country is landlocked and it would instead enter ground water.
Second, once the material is cooled enough to transport, it is supposed to be moved to a secure location, dropped deep into the ground, and encased in concrete. At this point if there are no earthquakes and water doesn't enter and damage the concrete, this will stay put for a thousand years or so, but eventually it will get out long before it's safe considering some of it takes around 250,000 years for it to decay enough to be safe.
As for what France does, as I mentioned, the US has not developed or built that tech because there is ultimately no profit in it and the US is unwilling to spend tax money on it. So it would fall to increased energy cost for the consumer in places where nuclear is used, and no one is going to like that. The cost of building the reprocessing facilities and doing the actual processing outweighs the value of the produced product. And building the first one is going to be the most expensive, and no modern energy company is likely to want to take the hit to short term stock prices in order to take it on. And conservatives won't approve tax increases at all in the current political climate. And progressive places have already started moving to renewables instead since it's cheaper.