I am a Indian passport holder resident in Botswana, I have UK visa, I am travelling and would like to visit France. Can I apply for French visa in UK ? Also can I also travel to Germany and such other coutries on French visa?
First, it is not a French visa but a visa of the Schengen Area. This is the visa policy thereof and I suggest you read it Visa policy of the Schengen Area.
Secondly, you can't apply for a Schengen visa in the UK unless you are a resident of the UK.
Basically, you require a Schengen visa and this must be done from Botswana (https://eeas.europa.eu/sites/eeas/files/infosheet_schengen_visas_botswana.pdf) or South Africa depending on the destination. I'm a visa required national myself (South African) but I reside in Ireland on a valid work permit and so therefore I can apply in Ireland for a Schengen visa.