[Elnino]

The alkene in trans-cinnamic acid should not hydrolyze in the presence of conc. H2SO4 right?

I was planning to run an esterification reaction of cinnamic acid but was unsure it would react.

[Babcock_Hall]

There are others here with greater experience than I have, but have you thought about the possibility of isomerization?

[Dan]

I take it you are worried about alkene hydration?

There will be a strong thermodynamic preference for the alkene since it is conjugated to the carbonyl and phenyl groups. Hydration (or addition of alcohol across the alkene during Fischer esterification) will be reversible and I expect the equilibrium to lie on the alkene side.