In OTR, the primary reason America became motivated to finish the canal was what happened during the Spanish-American War, when the USS Oregon had to sail 14,000 miles around South America to join up with the Atlantic fleet. Granted, it set a new record of making the journey in only 66 days, but during that time, people along the coast of Florida and the Carolinas were terrified that Spanish warships could just show up and start shelling them with impunity. Of course, what no one knew was the comletely terrible state the Spanish ships were in, unable to fight, barely able to steam at all.
So if the French had completed thier canal, I believe that the US would have realized that the defense of the nation rested solely on the goodwill of a foriegn power, the French, being willing to allow them to pass through the canal. This would be intolerable to Roosevelt, the man who's actions in creating the nation of Panama coined the term 'Big Stick Diplomacy'.
So would this lead to negotiations for the US to purchase the canal? Or, perhaps, leading to military action to seize both ends of the canal? By 1904, the US was in the midst of building a modern, big gun naval fleet to compete with the European powers. Maybe they would have been put to the test, acclerating the deployment of the new Dreadnought class ships that the US was so very slowly building. William Sims' ideas and innovations that could have revolutionized the American Navy might have found a more welcome reception if there were a naval conflict with the French Navy.
Would the French risk their battleships in a fight against the US? They had just seen their ally Russia get nearly their entire fleet destroyed by the Japanese.
And let us not forget the Japanese. They had just recently proven their competence in naval warfare by crushing the Russians in the Russo-Japanese war, and were a major worry for the US. If they saw a chance to exploit a situation where the American Pacific fleet had to be withdrawn from the Philipines to fight a war with France, would the exploit it?
The root causes of WWI came from battleship expansion, the first Superweapon, so could something like this lead to the war starting a decade earlier as a series of naval engagements?
P.S. Colombia's opinions in the matter would be given less thought than a gnat's fart. If you have no battleships, you have no voice.