Yeah, we forgot about Japan Air-- they definitely had a RTW route, but don't recall whether you could fly all the way around on one aircraft.
The 2/58 OAG shows Qantas flights to London:
via San Francisco arr Heathrow 1530 Mon and Thur
via Asia arr Heathrow 1430 Sunday, 1815 Tue, 1830 Wed (tourist only), 1645 Thur and 1530 Fri.
Departures from London:
lv 1100 Tue and Fri
via Asia lv 2200 Tue thru Sat; the Thu departure was tourist only.
The transpacific aircraft had a few berths; no mention of them on the India route. So you can see why I assume Qantas flights always turned at London.
In the 3/61 OAG, Qantas 707s arrived LHR
from Asia 1500 MoWeFr and departed eastward 1530 TuThSa. They arrived LHR
2115 SuTh from IDL and departed westward 1100 MoFr. (Qantas also had one Comet a week to/from Singapore.)
I'm guessing Air France never flew RTW-without-change, but they did have a RTW route network in 1974, if nowhen else: via Tokyo, Tahiti and Lima!