I am not a tax adviser but you say your father is not UK domiciled.
I would be worried that HMRC are asking questions about his house in France. If he is not UK domiciled HMRC should not be enquiring about assets located overseas as they would not fall under UK IHT anyway.
Are they fishing with the purpose of trying to argue that your father is UK domiciled?
I'd guess you’ve got yourself ahead of the actuality here.
It’s for OP (tim eyre) to confirm but my reading of his query is that he has not yet made any submission to HMRC/probate registry and so has had no response from them. His father died only earlier this month and as a first step Tim is asking in his OP for help about what are the correct UK forms to submit and how to fill in them in on the assumption that his father was not UK domiciled. Whether HMRC will agree to that assumption remains be seen and they may make enquiries –as they are perfectly entitled to do- which will obviously be helped if father’s NI number can be shown on IHT400 to confirm that there have been no UK earnings for about 40 years. However as OP indicates his father’s worldwide estate is likely to be less than £325k and under both French or UK intestacy law a large proportion will pass to surviving spouse, HMRC should not look to raise any queries over domicile as no IHT is payable.
What I suspect confuses OP is that IHT 400 asks for details of assets in worldwide estate; but in this case non-UK (French) domicile is claimed and so the value of only UK situs assets should be included. OP wrote that his father died intestate but from my very limited knowledge of such circumstances (one case only) I seem to recall the UK authorities will want sight of the foreign (French) letters of administration before agreeing to issue UK letters of administration - but I know a probate solicitor in England who does such Anglo/French intestate work regularly and who in addition could advise on the completion of the IHT401 to support the contention that France had become the father’s domicile of choice many years ago.
If your father has never been domiciled in the UK then his estate qualifies as an "excepted estate" in which case IHT 205 should be completed.
It is not clear from your posting although it does seem to suggest that at sometime he was UK domiciled?
My reading of OP was that father had a UK domicile of origin, had lived in UK until adulthood (probably marrying and OP Tim was son of that marriage), on the ending of that marriage had moved to France some forty years ago and had married a French national with whom he had a second family.