The word "race" carries a host of (usually negative) connotations in English as well, and in the wrong situation you can cause a commotion with it. Unfortunately it is the only word we've got that really means what you want.
I'm going to answer this with as little social commentary as possible, but just to be clear, races of humans are not biologically meaningful categories, but ethnicities can be sociologically meaningful.
A race is a distinct group of people, separated from others based on biological factors, usually skin color. It also often corresponds to place of origin or ancestry.
ex: Pacific Islanders or Australian Aborigines are often viewed as belonging to particular races.
An ethnic group or someone's ethnicity is a distinct group of people, separated from others based on sociological or historical factors. It may or may not correspond to race.
ex: Jewish or Hispanic people belong to particular ethnicities, but can be of any race.
If, conversationally, you chose to ask someone about their heritage, it would be safer to ask for their ethnicity than their race, and they would likely give you their race rather than their ethnic group.
However, in your example, worldbuilding, you are defining a group of people by their physical characteristics (and probably also by their social characteristics) so it would be appropriate to call them a race.
ex: In World of Warcraft, the Orcs are a race of green skinned warriors who value bravery in battle.
You would definitely use the word race in this context, as Orcs are a distinct biological population from Trolls or Elves or Humans. It would be trickier if they were all groups of humans who differed only in superficial physical characteristics, but people would be more understanding of the use of race in a completely hypothetical situation like that.