alternatehistory.com

In the aftermath of defeat, the French and Spanish were in shock, but their deficiency and decline in naval combat skills was revealed. Having lost experienced officers and quality to the French Revolution and lack of maintenance, plus ships to the major defeats of 1 June 1794, Cape St. Vincent, the Irish Expeditions of 1796 and 1798, the Nile and Hyeres along with various lesser defeats, it would be logical for France to abandon Egypt and Malta to defeat. Although a landing in Egypt was defeated when an amphibious invasion of Egypt with British and Ottoman ships began on 23 August 1801, other landings succeeded with the French being pushed into Cairo and surrendering by 9 December 1801. This would be followed by France losing Egypt with the surrender of Alexandria by 28 February 1802. Meanwhile, without resupply efforts, the island of Malta surrendered by 4 April 1802 to Britain. It would be the time for First Consul Napoleon to make peace with Britain, having won on Continental Europe only to lose the Mediterranean conquests of 1798 to 1799 outside of the Continent. Peace would be in effect with the Treaty of Amiens on 15 October 1802, but with Malta in British possession, it wouldn't last long, many ships of the French Mediterranean Fleet having taken advantage of the temporal peace to sail for Brest while Spanish ships returned to Spain.

In the meantime, France attempted to requisition Spanish ships for a voyage to Egypt, but the Hyeres defeat of France and Spain [by Britain under the command of Admirals Keith and Collingwood] would prove to be problematic and the attempt was cancelled. At least the convoy of merchant ships and all French survivors of the Nile that accompanied the defeated fleet were safe from capture. However, the naval defeat would result in command changes in France and Spain. Most captured ships from the Hyeres battle which returned to Britain would be repaired.

Treaty of Amiens terms were similar in this scenario to otl equivalent, but with more British dominance.