Short Answer: The story of the original Joes, in WWII. Operation GI Joe.
The term "GI Joe" was used in the sense of "your average soldier" since one of the several things GI has stood for-- with regard to the military (as opposed to, say, medicine)-- is General Infantry.
So the movie would trace the origins of Army's GI program during WWII. The idea is that, as one of the tactics of the war, soldiers seen as outstanding in some manner would be rewarded in a special way.
They would not be raised in rank, or given a command. Instead, they would be left right where they were, embedded within their units. But they would would be disciplined in front of their squads, to make it look like they kept getting sent for some punishment or even jail time.
Instead, during that time away, they were given amazing weapons and being trained to use them. They would look, to everyone else-- even their unit-mates-- like an average soldier, just a regular GI Joe. Even their souped-up weapons look like ordinary guns or other objects-- pens, backpacks, bandanas, etc.
So yes, a definite James Bond element. Also a touch of Captain America, in that seemingly ordinary soldiers who showed-- not greater strength, agility, or combat skill-- but greater bravery, initiative, or cleverness were secretly being looked at for special assignments. They didn't need to be stronger-- their weapons would be. They needed to be smarter and more willing to act based on the situation, rather than by the book.
In battle, the enemy would think they faced another squadron of ordinary soldiers with ordinary weapons, training, and ability. But then unexpected-- and unbelievably bad-- things would start to happen to the enemy. They would lose communications. Their planes' bomb doors would jam. There would be an earthquake-like tremor that knocked down their defense wall. They would not be able to figure out why they suddenly had so much bad luck.
Of course, we know it's the Joes, their scrappiness, and their hyped-up weaponry, doing all this damage.
Unfortunately, someone within the army grows suspicious. Let's call him Al. Why are these things happening? Does it have anything to do with the soldiers being disciplined? Where ARE they going, all that time? He decides to follow one.
Doubly unfortunately, an enemy soldier, whom let's call Dieter, also wonders if something is up, and he starts sneaking around also. Just as Al sees all the "punished" Joes going not into the brig but into a training facility, Dieter (who has been following him), catches Al.
There is a scuffle, and one of the Joes hears the noise, investigates, and sees Dieter drag Al off. Naturally, they have to save him, without anyone knowing that Al is gone or that he might know things. They also have to do this before Dieter gets back to his base and interrogates Al.
For the first time, all the Joes-- and just them-- team up to rescue Al. This becomes the first GI Joe mission, and is the second-last act of the movie. They use all their special weapons and learn to work as a team.
They also take code names. Some of these may be unique to this movie. Others, if appropriate, may presage the more familiar names fans of the series know-- the same way Nite Owl and Silk Spectre in the Watchmen are really the more technologically advanced successors of the originals with those names. Care will be taken not to compromise the canon set by the first three movies, but there is no way those who fought in WWII could still be young (and the same people) when the current series of movies is set.
Naturally, the Joes save Al-- but Dieter falls, hitting a rock with his head, and losing his memory.
Safely home, they ask Al what he saw. By now, he does not have to be told to keep quiet, but is the Joes' biggest fan.
The war ends, and so does the movie, with the Joes being made an official unit of the Army. Maybe, again depending on the plots of the existing film, they are given even more advanced weapons, and told that they are being sent against an increasingly powerful cabal calling itself... "Cobra."
