Plan 1: Reason with the titan. Tell it that although you have some booze with you now, you will be able to return with more in the future, if it lets you go now. Offer to let it keep the lippy elf hostage so you have an incentive to return.
Plan 2: Perform a montage with the frogmen and titans showing that it doesn't matter what species you are, you can all learn to get along and live together, if you will just forgive minor mistakes (like this one).
Once they are appeased, offer to share the glory and wealth of the elven empire with them. At first offer them simple goods, like clothing and booze. Once they start to trust you, get them to start smoking some assorted herbs. As time passes, smoking the herbs will become the norm, and the entire frogman society will be addicted.
Once they are dependant, the elves can restrict supply. Make up some story about how bad crops and all that. Prices will rise, and the elves can plunder the wealth of the frogman empire, ravaging their lands and emptying their stockpiles.
Once they are out of material goods, they will be given many tasks to perform in return for more herbs. Megaprojects can be built. They will have no purpose in themselves, but if the frogmen and titan are kept working hard, they will not cause many problems in the later stages of the plan.
The elves can then work on reforming the society and social attitudes of the frogmen. Although the elves and frogmen will be nominally equal, in effect the elves will be in a superior class in society. The goblin threat will be exaggerated (to provide a scapegoat) and the elves will be portrayed as all those keeping the goblin threat at bay. The news that reaches the frogmen will be heavily censored, and the children (being much more impressionable) will be doctrinated with elven teachings, and taught to be spies within the frogmen ranks.
A secret police will have to be established. They will look out for troublesome frogmen (who will be branded as "goblin spies"). Although not many in number, their successes will be well-publicised, and exaggerated. Those who might speak out will be silenced by the secret police, and those who have been brainwashed will turn in anyone who speaks out.
Once the society is stable, then the language will be changed. If the language is simplified, then the minds of the frogmen will be simplified with time. They will not be required for anything more than maual labour, so the frogmen language must be reduced to as few words and concepts as possible, with unfavourable concepts being eliminated from the dicionary.