Can't speak to ancient or medieval, but here are some modern/early modern examples.

There are many examples during the 18th century of artillery being captured and reused. For example, when Fort Niagara fell to the British in 1759, a sizable chunk of the French defenders cannon were captured British guns from either Braddock's defeated army, or Fort William Henry. Another really obvious example is Henry Knox using the captured British guns of Fort Ticonderoga to drive British forces out of Boston early in the American Revolution.

American forces re-used captured uniforms from the 8th regiment of foot just before encamping at valley forge, leading to the discovery of 8th foot buttons (a unit that never operated anywhere near VF) in the site's archaeology. Continental clothiers out of Philadelphia also noted issuing captured British uniforms of the 31st ROF to an American unit, Foreman's additional regiment, in 1778. On the other side of the fight, John Graves Simcoe in his journal credits a friendly fire incident in which one of his cavalrymen was shot while wearing a captured American dragoon helmet as being the reason he put the queen's rangers in those goofy leather caps with the crescents. Another potential, but not certain example of loyalists recycling Continental gear is the issuance of blue faced white coats to British Indian Department foresters at Fort Niagara, which might be captured coats from the fall of Fort Ticonderoga in 1777 (coats of that description were among the lost stores) but it's hard to say for certain that's where the Indian Department coats came from.

On the small arms front there are a number of references to both sides of the revolution using captured arms. After the battle of Trenton Continental forces captured thousands of Hessian muskets, which they reissued to a number of their own units. There are individual soldiers accounts in which American troops, dissatisfied with the French arms they'd been issued, would pick up British muskets whenever they had the chance. I once had an opportunity to handle a musket of the 17th regiment of foot that was captured at Stony point, re-issued to an American soldier, and ended up as a family heirloom until it was picked up for 500 bucks by a museum curator. And on the other side of the war, a unit of loyalists raised in Virginia at the very beginning of the war received, among other things, captured French arms from the French & Indian war that had been sitting in storage since that war's end.

Those are just the examples I can think of off the top of my head, but they speak to a willingness of 18th century armies to reuse captured enemy equipment. I'm not aware of any references to regular French or British troops reusing small arms or uniforms, but artillery seems to feature prominently. That said, it makes sense that a badly equipped force like the Continental army, bad certain loyalist groups, would be willing to reuse captured small arms and uniforms in a way more established militaries were not.