Yes, from how they worded the facts, it seems that at least during the period 1960-1974 J was labled "First".
The caravelle:
The seating layout in the Finnair version was initially for 16 first class and 57 economy class passengers.
DC8:
On 1 January 1966, Finnair opened an office in New York. In November, the company placed orders for two Douglas DC-8-62CF aircraft. This was a four-engine jet, designed for exceptionally long-range flights. The normal route version carried 16 first-class and 124 economy-class passengers.
The caravelle flew until 1983, not sure when the DC-8 went out of service.
Then again (even shown by recent "enhancements") it is not the name of the cabin that makes the class, it is what service they offer. Those "First" cabins may very well have been receiving very good service, even though we may laugh at the seats by modern standard. In those days flying was true luxury.