Should be able to access the latch mechanism from behind the plastic panel covering the inside of the door. It should pop off. The plastic panel should be held on by male clips around the perimeter of the cover. Once you have it open you can access the latch mechanism. However, there are metal door support brackets that make it tight to get into the actual latch mechanism (on the far right). The actual latch could be unscrewed from the end of the door and removed, if needed.
FIRST, I would inspect the actual plastic latch handle. Could be the plastic 'handle' that rotates upward when you pull on the door has either a rusted (frozen) spring or a part of the latch has broken off. Either case, you still have to remove the back plastic cover panel to remove the nuts securing these latch pieces to inspect/repair. A trip to the local junk yard is a quick and inexpensive fix if this is the case.
While you are there at the junk yard, consider grabbing some internal and external door handles as well. They are all made of plastic and sooner or later a piece will let go. It's easier to just go to your garage stash and grab a spare to make the repair than to continually run to the junk yard AND usually much cheaper than buying a new one on line or at the dealer.
