We live in Florida south near the beach: we grew several Jacaranda trees from seed in pots which grew to about a foot high and looked good. We moved them to a different place in the garden. We may also have over - watered them, but now their needle leaves have turned brown although their stems remain green. Is there anything we can go to save them?

Just another thought: Maybe its a deciduous tree and has gone dormant early due to the stress of moving and overwatering.

Jacarandas are deciduous, it is waiting for warmer weather, they also aren't cold tolerant so I cannot grow them even in zone 9

They grow like gangbusters here. One of the most common street and garden trees. Beautiful, MESSY flowers! Never plant them over concrete.
They are semi-deciduous, but haven't lost their leaves yet here. As long as the stems are green, you should be okay. Post some pictures so we can give more advice.

Yes, Jacaranda are deciduous. They are also hardy to about 19-20F. Especially established older trees. If a young tree is frozen back, they often return from the roots. We have a few mature Jacaranda around town here in zone 9A Florida. I have a young tree that I am grooming to plant out soon myself.
When I lived in Los Angeles, they were everywhere, in every microclimate. We had a few on my street that survived a RARE Christmas freeze we had to the low 20's for 2-3 nights without difficulty. The normal low temp for my microclimate in CA was 40-50F year round so never really warm. never really all that cold

I think the difference between Calif and Florida and here in Texas, is Texas constantly waffles temps with extreme high humidity and no air flow, (near Houston) as the Gulf winds lift up over Houston and creates a bowl.

Possible. I grew up between being in Houston at my grandma's house and being down at Rockport (near Corpus) at our own house. Lived on Galveston Island for almost 6 years as well. I remember Texas weather and how changeable it is