Not exactly. Washington picked a truly horrible site for a fort and was soon forced to surrender. He then signed an admission that he had killed a French diplomat, which was of course in French, so he probably didn't realize what he had agreed to.
George's career did not start off with promise.
You’re thinking of the Battle of Fort Necessity, which took place in July, 1754, about a month after the Jumonville Affair. Fort Necessity is a few miles southeast of Jumonville, along Rte. 40. And it is, indeed, a horrible site for a fort.