Looking to get back to Jakarta in late May (Business) I have asked BA GGL line to suggest routes, but mainly this are via Doha, which I want to avoid, also trying to avoid other ME3 Airlines and Turkish, BA to Sin doesn't start again until 1st June and HKG has a 10 hour layover

My question is if I bought 2 separate tickets, say LH Man to FRA and JL FRA to CGK would I be able to transit in FRA? or would be it be possible in AMS or CDG?

Thanks in advance for any advice