Here, par main barbare inhabitée can be translated as occupied by cruel or barbarian soldiers, and seems to include all fighting troops.

Interpretation

Naples, Palermo and all Sicily,
As well as the islands of Corsica, Sardinia and the gulf of Salerno
Will be occupied by barbarian soldiers.

History

The allies land in Sicily

The following excerpts do not describe a specific event. They rather show that the above towns and islands have been, indeed, occupied by the Germans first, and then the allies, after the landing in Sicily and Italy. From Nostradamus' perspective, they were all barbarians:
The port of Naples was one of those landing sites in Italy:
[P.448] The allied troops have reached the vicinity of Naples. The town people have risen agaisnt the german garrison. There is street fighting all over town and the death toll is quite heavy. (Par main barbare)

All Sicily was occupied by the Germans. The landing of the allies and the bombing of coastal towns by english and american aviation added to the destruction and loss of life the Germans left behind during their retreat:
[P.417] Sicily, target of the allies [June 1943]
Today, allied bombers have unloaded thousands of tons of explosive bombs [par main barbare] on Sicily, quite obviously preparing a landing, even though roman broadcasters keep on mentioning Sardinia as a possible landing site. A radio commentator has described the present situation as 'the most serious of our modern times'.
[Translation. - Chronique de la Seconde Guerre Mondiale, Jacques Legrand SA]

Marechal Albert Kesselring, commanding officer of the german forces «South» did not know what strategy he could adopt. As marechal Rommel did later on in Normandy, he hesitated between keeping his troops concentrated within the country or disseminated in small groups on the beaches in order to lauch a counter-attack (Par main barbare). He finally decided for the second solution: the Herman Göring Divison and the 15th Panzer Grenadiers were divided in four combat groups in order to cover the beaches from Palermo to Syracusa.
(Translation F.L. - L'histoire vécue de la Deuxième Guerre Mondiale - Book 4, P.690 - Christophe Lagrange)

The german occupation of Sardinia, Corsica and Salerno ended september 1943:
[P.224-227] According to a pre-established plan, the Germans [par main barbare sera inhabitée] left Sardinia for Corsica with the garrison of the 90th Panzer. September 12, Hitler decreted the evacuation of Corsica. ..As early as september 19, canadian troops were occupying Potenza, 50 miles east of Salerno; the plains of Salerno were in the hands of the 5th [american] army, and the battle for the bridgehead came to an end.
[Translation - Les Canadiens en Italie - Lt. Colonel G.W.L. Nicholson]

Note:
One must not forget Nostradamus must have found it extremely confusing, seeing all these troops fighting each other and throwing bombs from the air. As far as he was concerned, both the Germans and the Allies were barbarians.