How did france become the leading power of europe under the absolute rule of louis xiv?

since most of current immigration into the u.s., both legal and illegal, is coming from latin america. it would be very difficult to imagine or rationalize a country my fellow citizens are trying desperately to flee into, would pose a threat to my prosperity or freedom. since the u.s. has a long history of intervention, but no record of permanent occupation, i would not feel oppression is the main objective.  

the largest free trade nation, along with the largest gdp in the world wanting to expand it's economic policy on us, and including us, could only be positive. the u.s. government has no interest in, or way of simply forcing american culture on us. and has no track record of it. other nations that adopted american social culture, or "americanization" did so voluntarily, mainly through the choice of allowing american businesses and u.s. citizens to come into their nations, as free operatives.