'The troubadour style'? No, me neither. But here's how I came across the term.
While bimbling online, I came across the image above: an illustration from an unidentified book captioned 'Le comptesse de Tripoli et le troubadour Rudel. - 3me croisade 1888'. At the bottom left, the name CELESTIN NANTEUIL; at bottom right, LACOSTE AINE.
Célestin Nanteuil (1813-1873) was a not insignificant figure in the late Romantic period, a painter, printmaker and illustrator who was apprenticed with Dominique Ingres and became known as 'the Romantic engraver par excellence'. Another website mentions that he was 'a friend to such great novelists and writers as Alfred de Musset, Theophile Gauthier, Roger de Beauvoir and (most particularly) Victor Hugo, and illustrated many of their works with his fine etchings and lithographs'.
A bit more digging yields a reference to his nowadays being 'linked to the style called Troubadour', although 'preceded in this field by the brothers Deveria and especially by Alfred and Tony Johannot'. It would take a more assiduous researcher than me to tease out some of these art-historical strands, but 'Le Style Troubadour' is clearly A Thing. It has its own Wikipedia entry, for starters.
The description there talks of 'idealised depictions of the Middle Ages and the Renaissance'; the French art historian Henry Havard (1838-1921) had a bit of a dig when he waxed Gallic about 'that heterogeneous style which signals, to the indignation of all good people, the beginning of our century and which has been derisively called the troubadour style.' Notes for an exhibition in 2014, meanwhile, considered it a genre 'very popular with the general public but whose presentations are extremely rare'; a style that 'seduces as much as it can raise a smile through the staging of minor pages of History [...] and the valorisation of feelings', and adds: 'It was launched at the very beginning of the 19th century, in reaction to the neoclassical painters [...] with immense canvases where the heroes of Antiquity crush the unfortunate visitor under their assaults'.
The same notes evoke 'romantic crypts, forgotten lovers and fantastic castles' - and we begin to see where the appeal of the Rudel legend lay for the likes of Nanteuil. But this illustration is hardly the work of an 'engraver par excellence'; it more resembles a ropey effort accompanying a 1910s boys' own adventure story. Melisande in particular is bringing a 'pissed-off matron' energy to the tableau.
The culprit, of course, is not Nanteuil but the bottom-right-hand name: 'Lacoste aîné'. This is most likely Louis Conil Lacoste (1774-1837), patriarch of a family of Parisian wood-engravers whose work, according to the British Museum, is 'difficult to distinguish' one from the other. Le Style Famille, you could say. One assumes Lacoste was rendering from an original engraving or painting by Nanteuil, but I've been unable to find it.