Take a look at the document here. I refer to it later in this answer.
Whether you will have to pay the increased stamp duty or not depends on whether you are replacing your current main residence. Look at the chart in section 1.1. If you intend to sell your previous main residence within 3 years of buying the new one but don't so before the new purchase completes, then you will have to pay the increased stamp duty but so long as you sell your previous main residence within 3 years, you can make a claim for a refund of the additional stamp duty. The chart says 18 months but Osborne caved in to the buy to let lobby and increased the grace period to 36 months, defeating the stated object of the policy in my opinion. See section 2.8 to determine whether you are replacing a previous main residence. Section 2.12 states that foreign property is included in the property count for the purpose of the stamp duty increase.
I hope this helps but let me know if you have any further questions.
Your case is clearly not standard. HMRC will probably say that either the French property or the property you winter in is your main home. Section 2.8 gives the criteria that they will use to make the determination. You will have to get that sorted out so that you know which property you can sell within 36 months and claim a refund.