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Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
The recipient of a gift does not pay tax on it in the UK. As your mother is not a UK national, so long as she makes the gifts from non-UK sources there will be no UK Inheritance Tax implications for her estate when she dies.
You would need to seek advise as the French IHT position.
I hope this helps but let me know if you have any further questions.
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