This does nothing to the fission products. And reprocessing only lets you destroy the actinides if you burn them in a fast reactor. Fast reactors have, so far, been even more expensive than thermal reactors.
Fast reactors have been disappointing all over the world. The harder neutron spectrum is more damaging to materials, and liquid sodium has serious drawbacks. Fabrication of fuel elements with mixed actinides is also difficult. Fast reactors also require a higher density of fuel (due to the lower fission cross section at high neutron energy), which presents safety issues.
The french choice was clearly the wrong one. It's a net economic loss for them. It was predicated on the use of the separated Pu in fast reactors, but their experience with fast reactors was dismal.
If they weren't going to use the plutonium immediately, reprocessing was stupid. Spending the money they didn't have to, in order to make Pu they didn't need, just to have the Pu sit around, made no economic sense. And no, it doesn't improve the economics of waste disposal.
Understand where reprocessing came from. Way back then, the story was that nuclear was going to be dirt cheap, but would ultimately be limited by the cost of uranium. The solution was breeding, to provide all the expensive fuel those thousands of cheap reactors would need. Reprocessing was needed to close this fuel cycle.
But this story bears no resemblance to reality. Reactors turned out to be expensive, the number of installed reactors was far below projections, and uranium is not in short supply.
One still hears echoes of this old narrative from people who don't really understand where it came from, and why it doesn't apply.
Again, the only reason we're not all nuclear today is because of politics.