If you have a valid drivers license in the UK since over 2 years, you should be fine with most rental companies. You should make sure this will not be an issue when making your reservation.
French residents get a "life time" drivers license. It's difficult to pass the French driving tests, but then you receive a license for life. My grand-father is 93 and still drives...
I would be surprised, if any rental company, in France, had a maximum age policy.

We have contacted the following car rental companies, in France, with this question and specifically with your age 78.
Will update this page as responses are received.

Contacted rental companies with operations in France:
www.sixt.fr
Web Site: No maximum age.
Contacted by email: Minimum age 21 + license since 1 year minimum. No maximum age.
 

www.europcar.com
Web Site: No maximum age.
Contacted by email: Minimum age 21, No maximum age to drive in France
 

www.renault-rent.com
Web Site: No maximum age.
Contacted by email: Minimum age 21 + license since 1 year minimum. No maximum age.
 

www.avis.fr
Web Site: No maximum age.
Contacted by email: No maximum age. Drivers license since 1 year.
 

www.hertz.fr
Web Site: No maximum age.
Contacted by email: No maximum age

The results are what we pretty much expected. The French have a culture of respect for older people.
All rental car companies we contacted responded that they have NO maximum age policy.

All companies responded within 12 hours except SIXT, which responded 48 hours later. This was also half expected. SIXT probably offers the best prices of this list of car rental companies. Best price usually comes less service staff. If you usually require extra service, and can afford it, don't use SIXT.