As for speaking a foreign language, you need to take the jump. Know that, you are likely to be judged. However, there are people who find joy in seeing others speak their language and do so in a nurturing environment. You just need to find those people and practice with them, without fear of judgement.
Source: lifelong bilingual in French & English.
As cced already said, common ways of expressing this in American English include “don’t worry about it”, “no worries”, “no big deal”, “no problem”, “you’re welcome”, “my pleasure”, etc.
French also has more built-in structures for formal address/politeness, though many of them are being left by the wayside just as we left feudal lordships with a peasant class.
For what it's worth, I'd say that the more "stuffy" version of "de rien" in French would be "il n'y a pas de quoi".
From nothing is an overly literal translation. You'll hear it in Spanish for sure as de nada (of/from nothing) or por nada (literally for nothing) depending on context though.