From an earlier answer of mine also look at /u/fourthmaninaboat's answer to the same question for some of the bigger naval actions.

Most of the USN's surface encounters with the European Axis tended to be very small-scale compared to the Pacific battles and often entailed units smaller than destroyers after the North African campaign. That said, there were some battles that did take place.

A good many of these actions involved German torpedo boats (S-boats, also confusingly termed E-boats in some Anglophone literature and also not to be confused with actual torpedo boats, which tended to be larger than the PT-boat-sized S-boats) or other small craft intercepting Allied naval traffic. The invasion of Southern France did witness two small battles between USN surface units and German ships. The American destroyer Somers on 15 August 1944 engaged with two ships the Germans had captured UJ6081 (the former Italian corvette Camoscio ) and SG21 (the French aviso Amiral Sénès and sank them both. An American surface patrol engaged the Kriegsmarine two days later off of La Ciotat with the destroyer Endicott and two RN gunboats sinking UJ6073 and UJ6082. There was a more serious encounter off of Imperia in the Ligurian Sea on 2 October 1944 in which the USN destroyer Gleaves tangled with three torpedo boats engaged in offensive mining operations. This night action though was confusing and neither side understood the other's intents; the Gleaves captain initially thought fire from the German ships was from shore batteries and the Germans' commander overestimated the size of the Allied enemy they were facing.

Not all of the American surface actions in European waters were responses to German incursions. There USN was involved in offensive patrols to break up or destroy German sea traffic in France. While RN ships outnumbered USN ones, the Americans were present in these offensive sweeps and interceptions. The Kriegsmarine's 24th Minesweeper flotilla operated in the waters of the Gulf of St. Malo and the German-occupied Channel Islands. The 24th's principle American opponents were PT Squadron 30 and PT Squadron 34 which operated out of recently-captured Cherbourg. These PT boats operated with larger destroyers and destroyer escorts, such as on the night of 6-7 August 1944 when the DE Maloy and PT503, PT500, PT507, PT508, and PT509 tried to intercept German minesweepers off of Jersey. The American attack was not successful and the task force lost PT509. Six days later the DE Borum and PT500 and PT502 engaged with the Germans again with indecisive results. Borum and her PTs took part in a mixed RN force outside of Guernsey on 13-14 August against a small force of four German minesweepers escorting a merchant ship. Again, this battle was indecisive showing the difficulty of engaging in nighttime coastal operations with a veteran force like the 24th. The Channel Islands remained in German hands throughout the rest of the war and its naval forces could still get a few licks in such as when the subchaser PC-564 had to flee four minesweepers when its gun jammed and she had to be grounded at Pierre de Herpin 8 March 1945.

PC-564 and PT509 were not the only USN ships lost to German surface attack. One of the more serious battles in the English Channel was the S-boat attack on Exercise Tiger off of Slapton Sands in April 1944. Tiger was part of the training and rehearsal for Overlord and consisted of eight USN LSTs and a RN corvette for escort. The S-boats attacked the heavily-laden LSTs, sinking two- LST-507 and LST-531- and severely damaging two more. The cost of Slapton Sands was also quite severe with over seven hundred personnel lost and it caused minor concerns over security since some of the dead knew details of Overlord and it was not known if the Germans had picked some up as prisoners.

The S-boats also engaged with Overlord proper and the Cherbourg flotilla managed to sink a few USN LSTs and some other small craft. These attacks took place at night and were pinpricks to the larger Neptune fleet. Mines and obstacles were a greater threat to the Allied shipping in the region. German shore batteries, which were often manned by Kriegsmarine personnel, were responsible for the loss of the destroyer USS Corry off of Utah beach and the same battery likely sunk the patrol craft PC-1261, which some historians consider the first Allied warship lost to direct enemy action in Overlord.

Overall, the USN's contributions to the Allied naval effort in European coastal waters was minimal outside of merchant shipping. The USN had some heavy units involved in the main operations, but they supplemented the largely-RN forces which did the bulk of the heavy lifting. Vincent O'Hara estimates of the thirty-eight major engagements (in this case, O'Hara excludes small craft attacks like S-boats), the Americans were present in less than five percent of the engagements, coming behind the Soviet Navy. But while battles such as Imperia were not nearly on the scale of Leyte Gulf or the Philippine Sea battles, they were real enough for the men who fought them. The battle of Slapton Sands was by some metrics the last significant Axis naval victory of the war; the Kriegsmarine managed to interrupt and Allied training exercise and extract a high number of dead with no losses of their own. But Slapton Sands remained an exception rather than the rule for the Kriegsmarine's last year and most of their engagements were not as one-sided.

During Operation Torch in November 1942, the US fleet escorting the Casablanca, Morocco, landing force (aka Western Task Force) encountered Vichy French ships sortieing from Casablanca to intercept. The incomplete Vichy French battleship Jean Bart was moored in Casablanca harbor and lost a gun duel with the US battleship Massachusetts. The French squadron that sortied lost a light cruiser and several destroyers and submarines to the American task force. Source: Samuel Eliot Morison, History of United States Naval Operations in World War II, Vol. II—Operations in North African Waters, October 1942–June 1943. Boston: Little, Brown and Company, 1947.

As a quick response to act more as a prompt than a full reply, the US Task Force 39/99 and later actions by USS Wasp do play a role in easing the burden on Royal Navy. Late 41 early 42 is a difficult time for the Royal Navy. Prince of Wales and Repulse have just been lost and the Eastern Fleet now has 5 battleships and 2 carriers and is trying to hold on to the Indian Ocean.

Closer to home the German Navy looks like it is trying to muster its capital ship strength in Norway for a concerted effort against the arctic convoys based around the threat of Tirpitz. In the Mediterranean convoys still need to be forced through to Malta.

TF 99 was based around USS Washington and USS Wasp. Placed at the disposal of the British Home Fleet ostensibly to bolster the RN capital units against a major northern sortie at a time when the Royal Navy felt stretched. Later and in addition Wasp ran 2 important convoys of aircraft to Malta. Most of TF 99 rotates back to the US and then onto the Pacific after Coral Sea. But for that short space of time it represents a significant proportional increase in strength at a difficult time.