I was curious why the word for family in Swahili looked foreign, so I did my research and found out that the word for family in Swahili is "kaya". It was also noted to me that the younger generation tend to use the word "familia".
Source: My Tanzanian Swahili native speaker
I've also seen the word "jamaa" being used, but in a broader sense than just the core family. The basic meaning would be "relative", and so it would be used for the greater family, also including more distant relatives.
Thanks for your comment. I thought there must be a native Swahili word for family
I know the words 'Familia' and 'Jamaa' for family, I didn't know the word 'Kaya'. I found 'Kaya' to mean homestead. Somewhere else I found 'Ukazi' for residence. Both words are presumably related to 'Ku-kaa' = to stay.