I somewhat expect a GT6 announcement at E3. Too early for GT7, and as both Amar and Jordan have said, don't expect GT7 at E3.
The FIA Competition being fully revealed at E3 makes complete sense since there's 12 days till the end of Spring and E3 is next week (7+ Days).
Anyone remember the update that happened on the day GT Academy ended last year. 3 new cars and a new track. Based on that, it wouldn't be too farfetched to expect the FIA thing then, which is 6 days from now.
So, FIA Competition reveal at E3, playable in game in 6-ish days. That's what I'm thinking.