UK Tourist Visa for Indian Citizens from Paris

Yes, you will be able to apply for a UK VISITOR visa in France.

The controlling reference is 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.

Source: Part 1

The part about 'post designated by the Secreatry of State to accept...' refers in your case to the British Consulate-General in Paris.

Note that the rule explains that it works for VISITOR applications only. Other types of applications, like work and family applications are not covered by this rule. Work and family applications must be applied for in the county where you have established residence.

In order to apply you need to create an account at Visa4UK. You will also need to enrol your biometrics at a French station.

Update 3 September 2015

The rules changed in April 2015 and Paragraph 28 (quoted above) is no longer the controlling reference point. Everything is still the same, but they moved parts of Paragraph 28 to Appendix V of the rules. For an up-to-date answer that includes a confirming email from UKVI, please see Where can a tourist apply for a UK Visitor (standard) Visa?