The language names are adjectives in Latin.
From Hispanicus you get lingua Hispanica and the adverb Hispanice.
The name of the language itself is lingua Hispanica ("the Spanish language"), but typically the best choice for "in Spanish" is the adverb Hispanice.
The other forms of the adjective can come in handy, too; languages are simply described differently in Latin than in English.
What you need is a list of adjectives.
To get started, I recommend taking a look at names of countries in Latin.
The list in the answer includes the adjectives, so you can easily find what it means to speak Danice or Polonice.
Of course not all country names are associated with a language and there are languages whose names are not related to a country.