Health cards needed instead of EHIC card

That’s not what I said !

My advice to Karen would be to take professional advice based on HER circumstances - as previously suggested.

A very clear and informative post, I thought.
Should perhaps point out though that

only applies if the younger partner is a dependent.

In this case, the OP said in the first post that one of them is working, so would not be classed as a dependent. All workers must pay full social security contributions opposed to just health contributions. Social security rules for EU workers are very precise and need to be followed, especially in France because URSSAF has a reputation for coming down like a ton of bricks if it comes across a person living and working in France that it has no record of, who isn’t registered and paying cotisations either as a France-based employee or independent worker, and isn’t registered by an overseas employee as a posted worker.

The UK rules for residence are mighty complicated - it’s all to do with number of “ties” to the UK versus number of days spent there, can be anywhere from 16 days upwards. Simple summary here
http://www.pwaccounts.co.uk/latest-news/uk-resident-rules-defined/
France’s residency rules are far simpler, basically that either France is the centre of your financial interests, or it is where your family home is, or it’s where you spend most of your time. Obviously there are situations where both countries could consider a person resident, and the France-UK tax treaty sets out the steps for reaching a final decision. IIRC, in the unlikely situation where you spent exactly equal time and had exactly equal income, investment etc etc in both countries, then it comes down to whether you’re a national of one country and not the other. If you’re a national of both or neither I can’t remember what happens.
Fortunately residence is usually pretty simple, and it’s best to keep it that way, so muddying the waters by spending too much time in a country where you don’t want to be considered resident at that time, is best avoided as a rule.

@anon27586881 Yes, I was simplifying…we had to get HMRC to give us a view as our situation was not straightforward.