Translation:The candidates present their budget.
Yes, I think there is.
I am not 100% sure but I believe that, in French, when there are several owners and each owner has one «owned thing», you have to say it that way: «Les candidats présentent leur budget» (singulier) . (no danger that they have presented an agreed one!)
Imagine : «Tous les hommes sont invités à. venir accompagnés de leurs femmes» It sounds as if every one could appear with more than one wife. So, they say «accompagnés de leur femme»
Given that in English there is not a rule like this, we have to translate the French sentence into English as «their budgets». Otherwise, the meaning would be «many candidates, one budget» (possible... but so unlikely!).
I hope it to be understable, in spite of my poor English
The candidates present their budget is ambiguous in English. It could mean The candidates present a collective budget or it could be taken as The candidates present individual budgets (though plural budgets would be better here).
If I were doing this from scratch I'd be tempted by Each candidate presents his budget (her budget, for those inclined to insist on that), or The candidates present the budget for a collective offering.