It’s well known that, until the fourteenth century, French was the official language of England, and for several centuries thereafter England’s communication with other European nations was in French. But in the territory around the North Sea and the Baltic, where trade was dominated by the Hanseatic League, it’s more likely that in the Middle Ages such communication was in the League’s official language, Low German, which was probably mutually intelligible with Middle English (its oldest form, Old Saxon, is the direct ancestor of Old English), at least if English-speakers did not overload their speech with French-derived words.
As a result of this dichotomy, many English names of important places in this area and the lands to the north and east tend to be derived from their Low German forms (and quite distinct from their local forms): Norway (Norge), Sweden (Sverige), Copenhagen (København), Poland (Polska), Warsaw (Warszawa), Moscow (Moskva). And, a fortiori, such places as Brunswick (Braunschweig), where Low German was in fact the local language.
Elsewhere in Europe, however, including more southerly parts of Germany, French-derived forms predominate. In many cases the French form survives intact (the accents that might be found in modern French are irrelevant, and I will omit them when I give the French name): Cologne, Nuremberg, Munich; Berne, Lucerne; Seville; Turin, Milan, Florence, Rome, Naples, Syracuse; Prague, Belgrade; Thebes, Crete, Rhodes; Adrianople, Constantinople. The English pronunciation, of course, is what it would be if these were common nouns derived from Anglo-French. (In older times even more cities in the German-speaking world had French-derived names: Aachen was Aix-la-Chapelle, Leipzig was Leipsic, Basel was Basle.)
In some cases there has been a slight change of spelling to accommodate English conventions: Venice (Venise), Greece (Grece). Sometimes the French form has a final weak e (silent in English and in modern French) that is unnecessary in English: Lisbon (Lisbonne), Athens (Athenes), Spain (old French Espaigne).
There are also a good many cases in which the French name ends in a weak e and would produce an oxytone (a word of more than one syllable with the stress on the last) in English. English has traditionally avoided such names, and the tendency has been to replace the e with an a, giving a “schwa” pronunciation resembling that of Middle French (and of modern French as it might be sung, or spoken in Southern France). Some of the resulting names turn out to be identical with the native ones: Barcelona, Siena, Verona, Bologna, Messina. (Seville would seem to be an exception to this tendency, but in fact the traditional pronunciation is SEVil, not seVIL). But often the result is a peculiarly English form: Saragossa (Saragosse, Spanish Zaragoza, old Spanish Çaragoça), Geneva (Geneve), Vienna (Vienne, German Wien), Mantua and Padua (Mantoue, Padoue; Italian Mantova, Padova), Majorca (Majorque, Spanish and Catalan Mallorca), Salonica (Salonique, Greek Thessaloniki, Turkish Selanik).
Genoa is unusual in that it is based neither on the French (Genes) nor on the Italian (Genova), but on the Occitan form, while cities in the traditionally Occitan-speaking part of France are invariably known, as elsewhere in France (except for Dunkirk — see below), by their French names (Nice, Toulouse, and so on), except for the peculiar addition of a final s to Marseille (and also to Lyon).
Interestingly enough, some French regions that were once virtually independent states have English names that are distinct from the French: Brittany (Bretagne), Burgundy (Bourgogne). They are, instead, based on the respective Latin forms (Britannia, Burgundia). Latin-based names of historic regions are common elsewhere as well. There is, for example, Germany (Germania), and within the old German Empire, Saxony (from Saxonia, not Saxe or Sachsen, though the small Saxon duchies have Saxe, as in Saxe-Coburg-Gotha), Bavaria, Franconia, Westphalia, Austria, Bohemia, Moravia. In Spain there is Catalonia (Catalogne, Cataluña, Catalunya), while in Italy there are Tuscany (from Tuscania, not Toscane or Toscana), Apulia (Pouilles, Puglie), Sardinia (Sardaigne, Sardegna).
In the Low Countries, especially Flanders, where historically there has been a mix of Dutch and French, the English toponymy seems to be a hodgepodge. As an example, Ghent (Dutch Gent) was once called Gaunt (French Gand), whence John of Gaunt. Brussels is similar to the Dutch Brussel, but the final s points to its origin in the French Bruxelles (as in many other French words, the x is the result of a misreading of a medieval digraph for ss.) Neighboring Bruges (Dutch Brugge) is still known by its French name. Flanders, the name of the region, seems to be a blend of the Dutch Vlaanderen (a plural form) and the French Flandre (singular). Antwerp, on the other hand, looks like a singular form of the Dutch Antwerpen (the French is Anvers). Mechelen (the Dutch name, now commonly used in English) has also been known as Malines (the French name) and by the specifically English name Mechlin. Dunkirk, in French Flanders (French Dunkerque, Dutch Duinekerken), is perhaps the only city in France to have a peculiarly English name. And, further north, The Hague also seems to be a blend of the Dutch Den Haag and the French La Haye.
Now, if we move from Europe to the Eastern and Southern Mediterranean, the pattern changes. For place-names that go back to antiquity and have classical or biblical forms, English uses such forms, whether based directly on the original Greco-Latin (Syria, Damascus, Alexandria, Libya) or Hebrew (Lebanon, Jerusalem), or mediated by French (Tyre, Acre, Palestine, Egypt). But for places with a more recent history, curiously, Italian names pop up: Aleppo, Tripoli, Cairo, Morocco. The only places I can think of with distinctly English names are Tangier(s) and Algiers, and they are probably adaptations of the French Tanger and Alger, with the s added as in (the now obsolete) Marseilles and Lyons.