May be taking advantage of different winds aloft at different times in the day. The 777 shouldn't have any ETOPS issues with the great circle route.
It actually could be an ETOPS issue. ETOPS applies over isolated or rugged terrain as well as over water. Due to dozens of factors that relate to ETOPS, a twin-engine aircraft might take a longer route.
Long flights are sometimes filed as 2 flightplans. For example, LAX-HKG flights are often filed as LAX-ANC and ANC-HKG. If everything is OK approaching ANC, the first flightplan is cancelled and the second one started. This affects required fuel load, crews, etc. That might be what's happening on the LAX-CDG flights.
Just speculation, though.