British citizens do not require a visa for the Schengen Member States if the duration of their stay does not exceed 90 days within any 180-day period. Any stay that exceeds the 90-day period requires a visa.
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You do not need a visa for short trips to the EU or countries in the Schengen area if both of the following apply: you're staying for 90 days or less in a 180-day period. you're visiting as a tourist or for certain other reasons.
The UK is part of the EU but is not part of the Schengen area, a visa to the UK does not give access tot he Schengen area. That is why you had to get a UK visa not a Schengen one to enter the UK and why a UK visa has no use to you to go to Paris. As already stated above, you need a Schengen short-stay visa from France.
Schengen started in 1985 with just six countries. The UK opted out of the initiative, having much less interest in scrapping border controls because of its island geography.