Unless you are a full British citizen and therefore have EEA free movement rights, you will need to apply for a visa. The best thing would be to contact the French Embassy and clarify exactly what you need to do with them.
As you are a British Overseas citizen who has been living (I assume) legally in the UK since 1979, you are eligible to apply for full British citizenship. This would save any future queries regarding your need for visas. The rules on British citizenship were due to change next year. Whether they still will be under the new government or not is unclear, however you may wish to make your application now while the requirement are fairly straight forward as they may become increasingly more strict and the fees will inevitably go up.
I hope this answers your question in which case please accept. If you require any further information, please ask.
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