兴致勃勃 is adj that used only after "BE". ///eg. she's awake . Not: she is an awake girl.///so, it's not approperate to use it to describe"心态".///youcan use 好奇/轻松/紧张的 etc to describe “心态”///you can also say “我兴致勃勃地开始学习汉语” ：）

我以兴致勃勃的心态开始学习韩语? 语法上不算有错。但是一般不这么说。 “我兴致勃勃地开始学习韩语” 更好。

查词典可以知道： 兴致勃勃的意思是“形容兴头很高”。 我还是第一次听说“兴致勃勃的心态”这种组合，所以，我认为不可以，口语也不可以，因为它不是用来描写心态的。

No grammar mistake, it is okay for you to say like this. But for our native speaker, we are more likely to say "我兴致勃勃地开始学习韩语", using "兴致勃勃" directly as an adverb.

口語上可以說：我充滿期待的開始學韓文。