For
Osaka I have an answer ready for you...
You say 3 prefectures but the Keihanshin metro area consists of PARTS of 6 prefectures, so there's where you went wrong probably. Only Osaka prefecture is entirely part of the Keihanshin metro area. Some areas of Hyogo Prefecture (Kobe) and Kyoto prefecture are part of the MMA, but not all. And parts of Nara, Wakayama and Shiga prefectures are part of Keihanshin MMA aswell. Altogether some 19 million people on 11,170 km².
(Pink lines are the prefectures, blue coloured is the MMA)
Same for
London really.
There is no official definition for a metro area for London but the rather vague one from the GLA which puts it at 18 million. If you do the calculations this is comparable to a US CSA.
Just adding Greater London and Southeast England doesn't cut it though, because you are missing a lot of parts of the East of England region and including a lot of parts of Southeast England that are not in the London metro area by any definition.
For
Paris, Ile de France is not the metro area. Paris has an officially defined metro area (aire urbain) that differs in some places from IDF. It's about the same size though but is higher in population (>12 million). Probably the GDP is higher as well because it includes more urban areas and less rural.
Important to note is that French metropolitan areas are based on commuter percentages of 40% which is way more strict than the US Census definitions for MSA or CSA. Therefore, this is not really comparable to US cities even with the MSA definition or that 18 million number for London.
btw, it should be appearant that Paris with 11.5 million should not have a higher GDP than London with 16.5 million. That's a big clue that something is off...