Did The Louisiana Purchase take place when James Monroe was President?
No, it was under Thomas Jefferson.
James Monroe and Robert Livingstone were sent to France to negotiate a purchase of New Orleans and permanent rights to the Mississippi River. Napolean needed money and no doubt realized that the Louisiana Territory would be hard to defend and offered to sell it. The result was the Louisiana Purchase.
Monroe comes to mind ,but it was named for a steamer , the James Monroe, which was named for the President James Monroe , so indirectly it is named for a president. There is a town of Washington, LA, undoubtedly named for George in some way, either directly or after a man who took his name from George.
In 1802, Jefferson sent James Monroe to France to negotiate the purchase of New Orleans. Monroe and Robert Livingston (the US minister to France) accepted a much larger offer by Napoleon, agreeing to buy all of the French territory in the Mississippi Valley. This became known as the Louisiana Purchase.