Given the POD, that the French Imperial Army of 1870 would do which you write would be in my opinion like saying that the Army of Northern Virginia of 1864 would be able to rout the Union armies at every battle and besiege New York.
That the French could establish a defensive line at Wissembourg, why not. But that they would score as much victories against Prussia in northern Germany, definitely not.
At first, the Prussian military was far more advanced and disciplined than the French Imperial Army. At the contrary of Niel, Roon, Moltke and Bismarck had successfully reformed the army. The Prussians had for them a superior artillery and a faster and more organized mobilization plan. Concerning this latter point, it's especially more obvious when you see how the French mobilized; Prince Napoleon, while accompanying the Emperor said that 'generals were looking for their divisions, colonels their regiments...'.
The main advantages the French had were the Chassepot, the Reffye, and a greater capacity to endure a long war.
However, because of the secrecy that was built around the mitrailleuses, when they left the warehouses, noone knew exactly how to use them and had to learn while fighting.
In 1870, the doctrine of the Imperial Army was focused on defense; when offensives were attempted, they ended in failures (Saar, Sedan).
What's more, the French had an inadapted doctrine of use of cavalry as means of scouting, which was in part responsible for Wissembourg and Sedan.
What's more, you mention that Austria intervenes, but not Russia. Yet, Bismarck had signed a secret treaty with the Tsar, stating that if Austria was to enter in the war against Prussia, Russia would declare war to Austria.
Unless you consider a POD earlier in the reign of Napoleon III, you couldn't get something like that.
In my opinion, a stalemate is the better thing that the French could reach. If they manage to get the Germans into a war of attrition, the French would win in the long run, as shown IOTL during the 20th century.
I was surprised that no one mentioned the secret Russian guarantee given to Bismarck. It's quite obvious that the secrecy is more theoretical than real (what's the advantage of secrecy, if the main beneficiary - Bismarck - does not want a general war?): Austria knows about it, and they are also more than reluctant to support France unless there is at least an Italian guarantee of neutrality (actually they asked for a triple alliance against Prussia). It is also quite obvious that such an alliance is impossible (the Austrians are the traditional enemy, and France has squandered all the good will of 1859 by her meddling in the 1866 war and even more so by the refusal to recognise that the papal state is well past due date.
The French defeat was not created by Louis Napoleon military blunders, but rather by his political ones. After the Mexican (mis)adventure, the demostration of impotence in the 1866 war, the fizzling of the Luxembourg purchase and the internal troubles at the end of the 1860s, he needed a victory to shore up a tottering regime and insure the succession. Bismarck could read him very well, and knew that the Spanish succession crisis was a very good opportunity to push Nappy even more in a corner and force him to declare war. On the military side, the letargic pace of French mobilization quickly killed any possible hope to follor the original plan (which was to cross the Rhine and fight in Germany). It was not a very good plan anyhow, since the Prussian supply line was more secure and faster than the French one, so maybe not crossing the Rhine was a blessing in disguise. Then there is the better grasp by Prussian general staff of the changes in the way of fighting a war (the 1860s were an age of change, fast) and the undisputable superiority of the Prussian artillery.
Given the political and military scenarios (not to mention the personalities of the main players) I'd say that any kind of French victory would be paid long odds, but a complete triumph is absolutely asbish.