The French have seen their wages grow at 1/4 to 1/2 the typical rate of American wage growth for the last decade. They do not lack for collective bargaining.
The American median wage is higher than the German median wage. The Germans do not lack for collective bargaining.
The American economy and median wage has outperformed: France, Germany, Spain, Italy, Finland, Britain, among many other developed nations.
The American median wage is also higher than: Sweden, Finland, Netherlands, Germany, France.
The American median wage is so high, nations such as Britain barely qualify as matching up with our poorest states.
So much for your theory.