Thanks for your responses
To answer your questions
1) Will the gift by liable to inheritance tax in UK if my father lives for more than 7 yrs. and his estate is valued over the £325K threshold?
No, as 7 years sees any gift fall out of consideration for Inheritance tax.
2) Will inheritance tax by liable in France on me as the beneficiary if the gift is over the French threshold of 100K Euros?
NO, as you fall within the UK tax jurisdiction on the gift, as both you and your father are UK residents.
3) Will both of the above have to be paid - or only one of them?
Neither as advised above.
4) Income received by rental under French law could still go to my father tax free, however I presume that UK law would insist on treating this as UK income and it would therefore be liable to UK income tax in the normal way?
In the UK, the rental income will be treated as you and your wifes, as you are the legal owners of the property, are residents in the UK, and have a duty to report worldwide income to the UK tax authorities, so you will have the responsibility of declaring each of your half shares to HMRC after each 5th April.
I will accept your expertise in French tax law, that any money then paid to your father can be paid free of French tax - but I am sure you and your wife as owners will be liable to French tax on the rents, from which you can declare this French tax suffered within your UK tax returns, under the UK/French tax treaty we have, so you do not suffer tax on the same income twice. So please do check your tax position within the French tax jurisdiction.
5) Would the rental income interest on the property in France that my father retained mean that inheritance tax would need to be paid in UK after my father's death even though the property was fully owned by me?
Not in the UK no, as the property is not owned by your father, and you would have be liable to the UK tax on the rental income, so there again would be no IHT consideration within the rental aspect of this property visited on your father.
But as he would in essence be in receipt of income that is not earned (paid by virtue of a property not owned by him) then HMRC will be interested in the fact he benefits from payments of income, that will be treated as being paid from you (and your wife) and at face value, it would appear that you are repaying your father back for the initial gift (making this a loan rather than a gift) or that he is generating income. And this you perhaps need to consider further, as your father could face being liable to UK tax, on this additional income.
Do feel free to ask any follow up questions