1 You may be liable to CGT in the UK. The rules for calculating a gain are different in the UK from those used in France. Ultimately, whether you will have CGT to pay or not depends on the facts and figures of your case, in particular, the total period of ownership, the total period of occupation by you, the total period of letting, what the property cost to buy, the cost of any improvements and what it is sold for.
2 If the French property has been let, it cannot be your main home at the same time. As you own a property in London, unless you made an election within two years of having more than one home for one or other to be your main residence for CGT purposes, the determination of which is your main home will be based on the facts.
3 See 2 above. If it was accepted that the French property was your main home, then the London property potentially becomes exposed to CGT. You cannot have your cake and eat it I'm afraid.
4 There isn't much you can do other than sell it in a tax year when your incomes are low as the CGT you pay is determined by the level of your incomes. As the property has been let, you will be entitled to letting relief which can reduce the gain not covered by your occupation of it and the last 18 months of ownership of it by as much as £40,000 per part owner. See example 9 in HS283 for informtion on how this works. You use the exchange rates at the time of purchase and sale or the average rates for the tax year whichever is in your favour.
I hope this helps but let me know if you have any further questions.