* Trade surprised by USDA projecting smaller old-crop corn stocks

* Expectations of massive US crop caps corn futures rally

* Soybean futures see short-term rally, then head lower

(Adds analyst comments, adds bullets, updates headline, changes dateline from PARIS/CANBERRA, updates prices as of 1727 GMT)

CHICAGO, July 12 (Reuters) - Chicago Board of Trade corn futures rebounded off of multi-year lows on Friday, and soybean futures turned higher, as a government report forecast tighter stocks than traders had expected.

The trade was surprised when the U.S. Department of Agriculture projected old-crop corn stocks to fall below 2 billion bushels as feed and residual use increased - news that fuelled a flurry of short-covering, analysts said.

But corn's rally was muted by USDA's estimate of a monster U.S. wheat crop, which could vie with corn demand in feed rations, market analysts said.

"It'll also mean we could see an impact on corn demand in the export market, as people will buy more wheat from the U.S. as a feed substitute instead of corn," said Craig Turner, an agricultural commodity broker at StoneX.

Old-crop soybeans also turned lower later in the session.

Expectations of large U.S. grain and oilseed crops have been weighing heavily on corn and soybean future prices, which have dropped to levels not seen since 2020.

Friday's USDA forecast also predicted that the 2024/25 corn crop is poised to be the third-largest in U.S. history, with corn end stocks being the largest in six years as of September 2025.

Still, USDA estimated old-crop corn ending stocks would be 1.877 billion bushels, when traders had been expecting USDA to set the number at 2.049 billion bushels.

"We've been pressing markets lower for a while now," said Susan Stroud, founding analyst at No Bull Ag. "With these new lows we saw this morning, maybe we've officially reached a point where we've traded low enough."

Weakness in the U.S. dollar also gave grain and soybean futures a boost, traders said.

The most-active CBOT corn contract was up 0.73% at $413-3/4 a bushel as of 1727 GMT, while soybeans slipped 0.02% to $10.67-1/2 a bushel. CBOT wheat was down 3.28% at $5.52-1/2 a bushel, and dipping to the lowest since mid-April during the session. (Additional reporting by Gus Trompiz in Paris and Peter Hobson in Canberra; Editing by Rashmi Aich, Eileen Soreng, Varun H K and Frances Kerry)