(Rewrites to lead on soybeans, updates with USDA report, updates pricing, adds quotes, prior dateline: PARIS/CANBERRA)

NEW YORK, Oct 12 (Reuters) - Chicago soybean, corn and wheat futures rose sharply on Thursday in the wake of a closely watched U.S. government report forecasting a smaller corn and soybean harvest than previously projected.

The new harvest outlooks also fell below market expectations, helping prices recover from near three- and two-year lows for corn and soy respectively.

The Chicago Board of Trade's (CBOT) most-active soybean futures contract traded at $12.92 a bushel at 11:49 am CDT (1649 GMT), about 3.5% above its opening price and on track for its biggest daily gain in three and a half months.

CBOT December soybeans hit their highest levels since Sept. 29.

Corn futures were up about 1.5% at $4.95 a bushel and wheat futures were 13-1/4 cents up at $5.69-1/4 a bushel.

The U.S. Department of Agriculture's (USDA) monthly World Agriculture Supply and Demand Estimates (WASDE) report pegged the corn harvest at 15.064 billion bushels and the soybean harvest at 4.104 billion bushels.

It estimated average yields at 173.0 bushels per acre for corn, and 49.6 bushels per acre for soybeans.

"For beans, the headline numbers are certainly bullish there," said Jack Scoville of Price Group. "And we're responding accordingly."

If Thursday's USDA projects bear out, the corn harvest would still be the third-largest on record.

Despite the production cuts, waning export demand for both soybeans and corn was expected to leave an ample domestic stockpile, weighing on prices.

"It would be nice to see some more (export) sales coming in," said Sherman Newlin of Risk Management Commodities, noting that earlier on Thursday the USDA reported that exporters sold 295,000 metric tons of U.S. soybeans to unknown buyers.

On Friday, the USDA will issue weekly U.S. grain and soy export sales data, one day later than normal. (Reporting by Zachary Goelman in New York City; Additional reporting by Gus Trompiz in Paris and Peter Hobson in Canberra; Editing by Jan Harvey)