The Spanish-American war marked America's global coming-out party as a first-rate imperial power. It unseated one of the oldest empires, Spain, asserted American dominance in the Caribbean, and made inroads into Asia with the seizure of the Philippines.
How did the world, especially the incumbent European empires, respond to the new kid on the block? Were they nervous about a new rising power? Did they form strategic partnerships to counter the new threat across the ocean? What did America do to allay these fears?
France, it would seem, was very interested in the Spanish-American War as it had the potential to upset the balance of power and the status quo of the Old World - especially concerning the United States' occupation or presence in the Philippines. The French ambassador to the US, Cambon, would describe the War as the "second American revolution" which would extend the US's reach onto the world stage as well as set about the conditions for United States' imperialism outside of the Western Hemisphere. Cambon even feared with delayed negotiations, that the United States would set it sights on Africa or the Mediterranean.
Germany also had interests in the Spanish-American War. As a relative newcomer itself to imperialism, Germany had gained several territories in Asia and the Pacific. After Admiral Dewey's fleet entered Manilla Bay and defeated the Spanish fleet, five German ships led by Admiral Otto von Diederichs followed. Looking to capitalize on the potential power vacuum, Germany sought to establish a client state with the Filippino people which would allow for their independence and the ability for Germany to expand their influence. However, in the final negotiations regarding the annexation of the Philippines, the German government withdrew any sort of support to Spanish objections.
President McKinley as the lead negotiator for the conclusion of the war, did little to assuage European fears as Spain conceded to the United States' demands; however, the peace did ensure the US would mostly stay within the bounds of the Western Hemisphere and not upset the Old World status quo.
Sources:
Offner, John. "The United States and France: Ending the Spanish-American War." Diplomatic History 7, no. 1 (1983): 1-21.
Schult, Volker. "On the Way to World Power? The Emperor's Admiral: Otto Von Diederichs Between the Pacific and the Atlantic." International Asia Forum, International Quarterly for Asian Studies 36, no. 1 (05, 2005): 125-158.