I am a resident of Trinidad and Tobago visiting UK and want to visit Paris via Eurostar. What type of visa, if any, do I need?
As a citizen of Trinidad-and-Tobago, you do not need a visa for a short stay in the Schengen area, including France. You will of course need a passport and might be asked to justify the purpose of your trip, show you have sufficient means to cover its costs (e.g. a credit card) and return to the UK or otherwise leave the area.
If you are a resident but not a citizen in Trinidad-and-Tobago, then the rules depend on your citizenship, being a resident there makes no difference.