Wikipedia and Old-Computers both refer to PC-6000 and PC-8000 but all three IBM compatibles from Franklin Ace seem to be desktop models in the same form factor as the 5000, not all in ones.
What are the odds that Sears would've rebranded one of the other models already mentioned in this thread? Obviously not the Tandy's as you would have recognized that one, but perhaps a rebranded Amstrad or VTech Laser.
I worked at Sears when they sold the Franklin Apple and IBM knock offs. The IBM knock off's were desktop models, not all in 1's. They were 8088 with 640k of memory (maybe a tad more). They were nothing special and IMHO a rip off since I believe 286's were starting to come out at the time.
The Apple models were compact. I thought they were Laser's, but Im pretty sure we sold Franklin Apple compat models also.
We didnt sell many Franklin IBM compat due to price/performance/features. They were junk. We sold a few of the Lasers, but not having 100% compat hurt them. I pushed a # of people to get Atari ST's instead at that time from the local Atari dealer.