My garden is surrounded by a field where it's impossible to keep weed seeds out. I was wondering if I put in raised beds and then used gravel and salt in the paths would that salt leach up into beds? If so could I maybe put pond liner at the bottom of the raised beds with sand and drainage holes?

Is there any other way to keep weeds in paths down that's more long lasting? I could spray a bunch of roundup 365 but it'd be expensive and I'd have to reapply every year

I'm no expert, but a long time ago, I was talking with friends while waiting for our Philosophy Class to begin.
The Topic of Salting the Earth came up, and I remember hearing the most surprising thing.

Salting the Earth, while mostly symbolic of driving home the point of we have destroyed this civilization, its people, its land, and it will never recover....
There are in fact plants that can grow back in salted Earth. For your idea, its actually the opposite of what you want.
While making the paths bare, there are in fact weeds that can grow back. Anything you might want to grow later, probably wont happen, but some weeds still could.
In small amounts, like 2 to 1 water to salt in a spray bottle, it can be effective when applying directly to some weeds.
In large amounts, like the Romans driving home a point, I would not recommend. From what I remember it will eventually spread, widespread, its terrible for the land and soil, and eventually even after doing it, the only thing that might be growing back, would be weeds.

Without knowing what kind of square footage you are looking at, I've been told that one way to do it, is to put down newspaper for a time.
It blocks the light, moisture, and air, and any sprouted weeds will die.

I've only begun my Gardening Journey in the last few months, so take what I saw with a grain of salt. Sorry I just couldn't stop myself.

I think that the salt would leach into the beds over time.

I've used something like this weed barrier fabric, like below.
There's many kinds available I just took a screen shot of this Amazon product to show you.
It's usually sold at a local Home improvement center.
It's conveniently 3 ft. Wide, good for paths and then I put down some cheap Mulch to cover the fabric.
It won't last forever, but the ones that cost a little more do tend to last longer, (a few years)

They also make small metal (holders) to hold down the corners. They are actually (very large staples) made out of wire, is the only way I can describe them. Pic below.

Could you just mow between your raised beds? Or maybe lay down corrugated cardboard and straw to smother the weeds? I think if you use salt you will eventually come to regret it. And my personal experience with weed barrier/landscape fabric is that after a short time as many weeds are growing on top of it as there would have been otherwise (and it's a lot harder to do anything about them).