To try and cut a long story short :
Welles did not complete any of the Around the World with Orson Welles shows in time for their announced airing dates. He was months behind, inasmuch as he had signed for twenty-six shows to be shown every two weeks, beginning on September 23, 1955. As the series marked the very beginnings of private television in Great Britain, Associated-Rediffusion (the production company) and ITV did not want to postpone it. So the first two shows were aired in a nearly completed form, though lacking some minor elements. I don't know if Welles put the final touches afterwards himself.
When Welles left Europe to go back to the United States in October 1955, the one show (apart from the one on the Dominici case) that was utterly unfinished was the one on Saint-Germain-des-Prés. Welles probably had only shot the interviews with Raymond Duncan and the letterist poets, his farewell from a train (although there is no evidence that it was meant for this particular show), and possibly Art Buchwald (although there is no evidence that he meant it as a framing device). He also had shot his counter-shots for both interviews, but not his appearances as a host.
Welles tried to convince Associated-Rediffusion to let him finish the shows in New York. Associated-Rediffusion and Filmorsa accused Welles of violating his contracts and asked him to come back and finish the shows. (Welles was under an exclusivity contract to Filmorsa, Louis Dolivet's company. Filmorsa was helping Associated-Rediffusion to produce the series though it was not a co-producer in an actual sense ; some shows were edited in London, some in France). Associated-Rediffusion asked Filmorsa to complete the Saint-Germain-des-Prés episode if Welles were not to come back. Among the shots added then :
— a couple of shots with a Welles double (or doubles) ;
— shots taken from a short film directed by Jacques Baratier, Désordre (“Disorder”). They include shots of Cocteau, Juliette Greco, Simone de Beauvoir and other celebrities, as well as numerous nightclub scenes ;
— shots of Eddie Constantine probably coming from one of his feature films (Filmorsa had just signed Constantine) ;
— typewritten introductions to the shots of the celebrities ;
— reaction shots of Welles taken from other shows in the series.
Welles's cut of the Basque episode is the one devoted to the “pelote basque.” The other version (the one in which Welles and writer Lael Wertenbaker compare American and Basque systems) was edited after Welles had left Europe. It was the “pilot” offered to American TV.
There also were two versions of the Madrid episode, although one of them is not available for viewing anymore.