The English spelling of the French cities Lyons and Marseilles preserves an orthography still current in France in the 19th c.:
le colonel Mocquart …, avec ses hommes, sa retraite jusqu'à Lyons. — J. Stevenin, Rapport sur les opérations de la compagnie des francs-tireurs d'Elbeuf pendant la campagne 1870-71, Elbeuf, 1872.
Col. Mocquart … with his men retreated as far as Lyons.
SALSEPAREILLE D’EUROPE (Smilaæ aspera), dans les environs de Perpignan; fossile dans les dépôts miocènes du bassin de Marseilles. — Explorations Pyrénëennes 11, 1876.
…in the vicinity of Perpignan; fossil in the miocene deposits in the Marseilles basin.
Reaching a plural Algiers requires returning to the 17th c.:
& j'ay appris d'un Jéfuite qu'il avoit veu dans Algers une Bibliotheque fort ample, dont le Roy luy montra plusieurs Volumes ;
And a Jesuit tells me that in Algiers he had seen a quite ample library where the king showed him many books. — Pierre Le Gallois, Traitte des plus belles bibliotheques de l'Europe, Paris, 1685.
The name in Arabic, Al-Jazā’ir, is a plural meaning ‘the islands,’ which may explain the spelling which English retained.
The present day Tanger still had an s in the 18th c.:
Le Commerce des Anglois dans la Mediterranée, étoit fort diminué dépuis que nous fumes obligez d'abandonner Tangers en 1685. Lettre écrite de Londres le huit Juillet 1706, La Clef du Cabinet des Princes de l’Eutope, Aug. 1706.
English commerce was strongly diminished after we were obliged to abandon Tangiers.
…en vertu de l'Alliance qu'ils ont avec les Anglois , ont permis d'acheter quelques bleds à Tangers & à Tetuant, pour les biſoins de cette Garniſon. La Clef du Cabinet des Princes de l'Europe, Mar. 1710.
…by virtue of the alliance they have with the English they allowed the purchase of some vacant land around Tangiers and Tétouan for this garrison.
il [Charles II] se plaignit de ce qu'elles avoient refusé les subsides nécessaires pour la défense de Tangers… — L’Angleterre instruisant la France, ou, Tableau historique et politique du règne de Charles Ier et de Charles II, London/Paris, 1793.
…he [Charles II] complained about those [in Parliament] who refused the funds necessary for the defence of Tangiers
… il fit marcher un considérable corps de Troupes pour faire le ſiége de Tanger , où ce Gouverneur s’etoit retiré. Ces troupes mal diſciplinées, & peu ſoumiſes à leurs Commandans , s’approcherent de Tangers, mais elles refuſérent d'en faire le ſiége… — Suite de la Clef, ou Journal Historique sur les Matieres du tems, May 1736.
…he had a considerable corps of troops march to lay sieze to Tangier, where the governor had retreated. These troops, poorly disciplined and barely obedient, approached Tangiers, but refused to lay siege.
The identical pronunciation with or without the s likely explains why both spellings occur in such close proximity. This does not, however, apply to English:
The American minister's statement to the French Government, that the United States had sent warships to Tangiers only to assure the release of the prisoner, was taken as recognition of the special position of France in Morocco.10 The foreign colony in Tangier, panic-stricken because of the Perdicaris incident, appealed to the French for protection. — Raymond Walter Bixler, The Open Door on the Old Barbary Coast, 1959.
Since this is the only place in the book where Tangiers appears, I assumed it was because of the spelling used in the cited work. The endnote leads to two issues of the Foreign Commerce Yearbook: 1949 uses Tangier, and 1951 Tangiers.
Though a Google Books NGram shows a preference for the s-less variation, both spellings have a long tradition. Correspondence to and from the court of Queen Elizabeth I was happy with both:
As the Portuguese business is entirely in the hands of the Treasurer, the earl of Leicester and Giraldi, it is difficult to get particulars, although I am told that the latter was willing to concede, on behalf of the King, that the English may trade in Barbary, so far as regards Ceuta, Tangiers, and Mazagan, but the English claim to trade everywhere north of Cabo Blanco. — Letter of Intelligence from London (unsigned) to the Grand Commander of Castile (Don Luis de Requesens y Zuniga), Governor of the Netherlands, 1 June 1574.
The five Governors of Portugal have dispatched commissions to all their signories both in the East Indies and in Africa, willing their governors to have great care of all their charges, and in no sort to resign them into the hands of any whatsoever without the great seal of Portugal, what other warrant soever shall be offered to them. Tangier and other towns in Africa have answered, assuring the Governors that they will perform their commissions to the uttermost. — Letter, Ralph Lane to Burghley, 21 Mar. 1580.
Moreover the ‘distress ’ which Don Sancho d’Avila had suffered in Africa is veriﬁed by those letters, as also that two alcaldrs of the King of Fez had been received at Tangier in Africa, by whom it was reported that the said king had sent an ambassador to the Turk with rich presents. — Cobham to Walsingham, 27 June 1582.
The King of Portugal made a great brag to conquer the whole of Barbary, and as the King of Spain refers all his doings to his Council so the King of Portugal will do all as he lists of himself, and so went to Tangiers, where he found the Moors too strong and so was fain to return. — Letter, Roger Bodenham to Lord Burghley, 16 Nov. 1597.
The presence of an s in a French name need not mean a plural. Old French maintained a two-case system — nominative and oblique — where most Latin neuters merged with the masculine. The nominative masculine singular had a final s, like the forenames Georges, Charles, and Jules. Now I am not schooled in Romance historical linguistics, but I imagine this may have something to do with how Londinium, the Latin name for London, became the French Londres.