I am a British citizen. I was born in Britain, but I have Mauritius passport. I would like to do a return trip to Paris on the Eurostar. Can I use my Mauritius passport?
According to this and other sources: https://ec.europa.eu/home-affairs/sites/homeaffairs/files/what-we-do/policies/borders-and-visas/visa-policy/apply_for_a_visa/docs/visa_lists_en.pdf
A Mauritius passport holder is allowed to visit France (Schengen area) and stay for up to 90 days within a 180 day period without a visa.
You need to ensure that you have sufficient funds for your stay and accommodation and travel insurance.
As you are UK resident, then I suggest that you ensure you have documentation of your UK status to prove you links to the country if required.
Contrary to the suggestion in another answer, proving links to the UK will not be necessary beyond proving your UK nationality, because EU freedom of movement is still in place during the transition period. The main problem you will likely face is that you will most likely have to prove your UK nationality when you return to the UK, because if the immigration officer decides to question the purpose of your visit (a standard question), you will be unable to satisfy the criteria for entering as a visa-exempt visitor. You will then need to establish that you are a British citizen or else they will either send you back to France or remove you to Mauritius.
Obviously, a UK passport is the best way to do this, not other official evidence of your nationality will probably suffice.