Can I keep canned peaches in the fridge if water got in during processing?
Yes, basically anything cooked will last at least a few days in the fridge.

If you want it to safely keep it longer than that, you can freeze it. It's probably best not to try to reprocess the jars though, since you don't know exactly how much water got in (and how much acid and sugar got out), so if you're unlucky it could upset the recipe enough to make them unsafe.