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You can apply for a UK Visitor (general) visa in any country that you entered legally. The only stipulation is that you must remain outside of the UK while your application is being processed and there must be a designated issuing post in that country. Nationality of the applicant does not matter.
This is covered in Paragraph 28 of the rules...
An applicant for an entry clearance must be outside the United Kingdom and Islands at the time of the application. An applicant for an entry clearance who is seeking entry as a visitor must apply to a post designated by the Secretary of State to accept applications for entry clearance for that purpose and from that category of applicant. Subject to paragraph 28A, any other application must be made to the post in the country or territory where the applicant is living which has been designated by the Secretary of State to accept applications for entry clearance for that purpose and from that category of applicant. Where there is no such post the applicant must apply to the appropriate designated post outside the country or territory where he is living.
All UK posts in the Schengen zone (including Visa Facilitation Centres) are designated to accept visitor applications (but they sent to and are processed at the hub in Paris). So France is ok and the answer to your question is YES. See Paragraph 41 of the rules for information on specific requirements.
From a practical viewpoint as someone travelling in Europe, you may want to consider if you have all the needed evidence to hand and can do with not having your passport for a while. If not, then it may be better to wait.