Literally meaning Frankish (or French) language in either Italian, Latin, or a hybrid thereof. It usually references the most common language spoken within a group.

I've heard three different stories of how the phrase 'lingua franca' came to be.

One was that a hybrid language, heavily French but including parts of everything else, was spoken in Mediterranean ports (where most mixing of disparate languages happened). In order to do business there, you had to know the 'lingua franca', the name given to the language. The phrase grew out of that.

The second way that I've heard this phrase was created was that, at the time of the Enlightenment, France was the scientific center of the world. All published papers and ideas were exchanged in French. The Latin (if it is Latin) phrase 'lingua franca' grew to express the need to know the common language between scientists.

From there, it appears to have gained a political definition - French was the standard language of diplomats and politicians in Europe and the surrounding countries. (I certainly hope I'm correct here - some sources cite diplomacy as the first source, and others don't mention it at all...) And, once it entered a second sphere of influence, it spread into daily use.