Read the help sheets on the IR web site,
Having accommodation hasn't been relevant since about 1994.
Registration in France wouldn't affect the UK tax treatment, except if you would otherwise be taxed twice.
Well, sort of. You are still liable for investment income arising in the UK, but you get the normal allowance so unless you're very well off you won't owe any tax. You are also still liable for capital gains tax unless you're away for 5 years.
As a concession they normally agree to start the non-residence from when you leave, so probably none of the income you had in France will be taxable (in the UK at least).
The IR residence leaflet is fairly helpful, you should be able to tell from that if you fulfill the rules unless there is something unusual about your case. IIRC the basic rules are that you have to be gone for at least a complete tax year, you have to average less than 90 days a year in the UK, and in any case less than 183 days in any one tax year.