Greetings! This is certainly one of those topics which remain debated to an extent in historical academia regarding the First World War. It certainly does not quite fit into the whole rosy "America entered as the saviour of democracy and humanity" narrative which has often been propagated by the postwar education and (to an extent) continues to this day. For some contextual background on what America was like before the "critical year" of 1917, American First World War historian Michael Neiberg has two rather good lectures on the matter: one found here about the decision to go to war, and another here about the period 1914-1917. Before we begin our own little discussion on the economical factor of America's entry into the Entente Powers and the First World War, it is necessary for us to tackle a few key concepts and ideas:

The Cultural Argument

Firstly, OP's description of the cultural ties which may have played a role in America's entry into the war relate to the geopolitical relations it had with the French and British government at the time of World War I. This motivator has often been scrutinised by historians, and the general consensus is that there were no significant cultural sentiments which propelled the US Government to declare war against Germany rather than Britain and France. President Woodrow Wilson viewed both the French and the British as "old-world imperialists", and especially despised the British governments "navalism" (a reference to its use of the Royal Navy to aggressively conquer and control colonies). To Wilson, this "British navalism" was just as bad as "German militarism", and much of the American public also shared this viewpoint at the beginning of the war in 1914.

The American public itself was divided by 1916, with two clear sides forming (albeit minority sides, as neutrality remained the major sentiment up until 1917). On the one hand, America was full of ethnic German-Americans, whose vote Wilson may have wished to secure by promising neutrality in the coming years. There were also Irish voters in the Eastern cities, whose fury at the British oppression during the 1916 Easter Uprising meant they were against the US joining an old enemy. On the other hand, the Pro-British side was formed of the "Wasp" (White Anglo-Saxon Protestant, as Michael Howard terms it) supremacy on the east coast, as well as notable figures such as newspaper magnate William Randolph Hearst and ex-President Theodore Roosevelt. Neither side could claim the majority up until 1917, so America had to remain politically neutral in the whole affair. Thus, was there a cultural link between the US and the Entente that weighed in heavily on the intervention debate? Not to a significant degree. The main "cultural" factor (if it can termed as such) which may have played a role was the news of German war crimes, most notably the atrocious acts committed by German troops in their occupation of Belgium, and their deliberate destruction of many cultural/religious sites in the Low Countries. News of these atrocities is believed to have tipped the scales further in favour of American intervention on the Entente side, though as we shall discuss next, the economic factor was a considerable one.

The Economic Argument

Secondly, this bit of OP's explanation of the question requires a bit of clarification:

"Geographically it’s easier to hit France and Britain’s ports. So we allied ourselves with them."

For the purpose of this response, we shall take "hit[ing]" the ports to mean that the US found it easier during the war to advance its economic interests in the UK and France rather than Germany. This point stands fairly well, though this was mostly due to wartime fact rather than commercial preference. France and Britain relied to a considerable extent on shipments of American goods to sustain the war effort, and the US was more than willing to extend credit to these countries and continue the flow of materiel. On the other hand, the Royal Navy's blockade of Germany meant that no US goods were able to flow into that country. This of course created a natural "tilt" towards the Entente Powers, and gave the traders in America more to worry about as the war dragged on. Michael Howard sums up this economical perspective well:

"Yet as the war went on an increasing amount of that business [America getting involved in war] consisted in supplying war material to the Allies - not necessarily out of ideological sympathy, but because they could not get it to the Germans. If that trade were interrupted, then the war would become their business, whether they like it or not."

With the recent historiographical work on the matter, we now know that key advisers and business officials in America did indeed share concerns about a German victory endangering the economic expansion and security of the United States. In the 1920s and 1930s, "revisionist" and "New Left" historians contested that the economic security of the United States, coupled with the threat to that security posed by German unrestricted submarine warfare, led the American government to choose intervention over neutrality.

There is certainly some merit to this argument. The war-induced exports boom to the Entente Powers was a great boon to the economic power of the United States, and its businesses did not mind being unable to trade with Germany so long as Britain and France continued to place orders for resources and war materiels with them. By 1917, exports alone made up 11% of America's Gross National Product (GNP), and 80% of that trade was destined for Entente ports in Britain, France, and their colonies. There is a positive correlation between the US public's outcry at German submarine warfare and the rising export boom throughout the war. In 1916 for example, when both exports and the German submarine threat were far greater, Wilson threatened to sever relations with Germany if they continued (and the German government actually abided by this warning, suspending unrestricted submarine warfare until January 1917).

The Geopolitical Argument

There were however, other geopolitical fears which may have fitted nicely with the economic ones, but did not necessarily include them. As early as 1916, Wilson's advisers (chief among them Colonel House), were fearful that a German victory would lead to serious problems for America's own position in the world. After a visit to Europe and talks with the Imperial German government in 1916, House remarked:

"If victory is theirs, the war lords will reign supreme and democratic governments will be imperilled [sic] throughout the world."

Wilson for his part, was an ardent supporter of neutrality, and he wished to keep America neutral for as long as the war would permit. By 1917 however, it had become clear that a German victory might very well be a possibility, and after failing to bring both sides to the negotiating table (with the German peace terms being so outrageously unacceptable that even their Chancellor had to present a "scaled-down" version to the imperial parliament), Wilson concluded that "Prussianism" was the gravest threat to America's security and continued prosperity.

With the removal of Russia from the war, the American public began to realise that of the two sides in Europe, there was a lesser evil. They had seen propaganda posters and news reports of the horrific German atrocities in Belgium, the use of poison gas, and the POW camps. The LIFE magazine (a satirical one, not the one we have today) even circulated a cover in 1917 of a picture of the American states "if Germany won the war". Fascinating image by the way, worth a look and analysis here. So clearly in 1916-17 we have a clear lean of sympathies towards the Entente and the Anglo-French nations, but how did this translate to American involvement?

It all came to a climax in the Spring of 1917. We of course have the Zimmerman telegram which was published in the American press and read like a declaration of war (despite the fact it was anything but). We also have the German decision, after much internal and external discussion, to resume unrestricted submarine warfare. Once these two events had occurred, the fuse was lit. It was only a matter of Wilson deciding to declare war, which he very reluctantly did on April 5, 1917.