Nicknames for foreigners come in various shades of offensiveness, and in theory the least offensive are those that pick on a familiar name like Paddy or Taff, or ape the language spoken, which makes Russians Russkies and the Chinese Chinks; while the worst are the merely abusive ones like "Wop", which seems to have come from the Italian for a ruffian, or possibly from the Latin for a no-good, and "Hun", an archetype for barbarism. In between come the names that have to do with food, or what your true patriot calls foreign muck. "Krauts" for Germans (also "Limeys" for Brits, because our sailors sucked limes) comes in this category, and so, one would think, does "Frogs".
But it doesn't work like that. The theory puts "Yid" among the milder insults, but in practice it's one of the rudest. And the history of "Frog" is not so simple. The OED says froggy is a term of contempt for a Frenchman, from their frog-eating habits; but under frog we also read "A term of abuse applied to a man or a woman" (French or otherwise), though it gives no examples later than the 17th century, when it applied to Jesuits and Dutchmen.
Anyway, I doubt whether the Daily Star is worried about word origins. Calling a Frenchman a Frog is neither more nor less offensive than calling him a Frenchy or an Italian an Eyetie. Such names were common enough in middle-class society before and after the Second World War. Now they live on only in the fantasy world of the ultra-popular press.