Staying in Europe for longer than 90 days

Your partner of course has no problem as being a citizen of an EU country means being able to live anywhere in the EU indefinitely.

However, a UK Ancestry visa carriies no such rights, and as I understand visa free travel over and above the normal duration to France requires residency in the UK with the ccorrect endorsement. However, this is not valid for business trips, and we always tussle here with whether house sitting is employment.

This French Consulate site goes through some of the details: http://www.ambafrance-uk.org/Visa-applications

The immigration police will not ask about the date of your return to Australia when you enter the EU. Your problems will come up when you leave the EU in the form of questions and fines.

If I were you, I would make an appointment with an EU country and apply for a visa that applies best to your situation.

Thanks for the responses
Since I am a partner of an EU person don't I get the same rights (i.e. the ability to stay in the Schengen Area indefinitely)?

Don't think so. Maybe if you were married.

Best advice, ask the appropriate authorities.

Not for France according to the above link unless you are resident in the EU. Some more advice here: http://europa.eu/youreurope/citizens/travel/entry-exit/non-eu-family/index_en.htm

"Since I am a partner of an EU person don't I get the same rights (i.e. the ability to stay in the Schengen Area indefinitely)?"

Absolutely not.

If you are married to, and living with, an EU citizen you are allowed to live with them and work anywhere in the EU. If you are not married, hard luck. Your EU-citizen partner will need to fill out some paperwork to register herself as resident in France. This would be the same paperwork that a French citizen would have to fill out.
You wrote "You could call us self-funded retirees", if this implies you are being paid, that is working, then you are not only breaching your 90-day tourist limit, you are also working illegally.
"send us back home" - they could send you back home; but since your partner is an EU citizen, she can't be sent "home" (which would be the UK anyway).

There is only one solution - wedding bells :-)

To further clarify, you can't just show up in Europe with your EU spouse and expect to be considered "legal." There is a process you need to go through with the local authorities to verify the relationship, etc. If all checks out, you could be given residency in the form of a card which will specify your ability to work. I have many US colleagues who are married to Austrians, for example. To work in Austria and to live here legally, these US citizens must go through a lengthy process with the local authorities to receive permission to reside and work here. Several have had to go and come from the US as they were unable to sort this out within the 90 day timeframe for US visitors.

Your partner of course has no problem as being a citizen of an EU
country means being able to live anywhere in the EU indefinitely.

Well to start with this is a common misunderstanding of the free movement of peoples rules - an EU citizen does not automatically have the right to live anywhere in the EU!!! The relevant legislation is EU Directive 2004/38/EC

An EU citizen has the right to reside in another EU country for up to three months while seeking employment and if successful they will be allowed to establish residence there. If they fail to find a job and are not granted a further three month extension, then they must return to their own country.

Alternatively and I expect this covers the OPs situation, if the EU citizen is no longer engaged in an economic activity and derives their income from pensions, dividends royalties etc... then they can establish residence in another EU country provide they will not be come an economic burden on the state.

OP assuming you are intending to reside in France here is the jumping off point. In this case your EU partner should register at the town hall in the location where the house is. Provided you can show sufficient funds and medical insurance, they should them be able to apply for a permit for you as well.

However having said that you should be aware that you will no longer be considered a tourist and as such you will be subject to local taxation and social security rules. So you should carefully check the impact that will have on your income etc. before doing this.

Yes indefinitly was a bit of hyperbole and a half if taken completely generally without considering the full circumstances but beyond three months is fine if you are on your own resources and not going to c!aim on the social security of the country you are in which seemed likely to be the case of the OPs partner. Registration would be needed though in most countries.