Hi Patrick,
I believe Vacuum full rebuilds the indexes automatically by default, as a new copy of the table is created.
Because the indexes are new, no stats are available to the optimiser to make an informed decision about whether to utilise it or not, so it doesn't.
Once the analyze is performed as Venkata said, the stats are available for it to make that decision. So, you didn't really need to build the indexes again.
Hope that makes it a little clearer.
Cheers