Do OAPs get discounts for the various taxes (foncier/d'habitation, and others) and other outgoings in France. If so, what does it amount to?

Potentially yes, but whether or not you qualify and how much discount you get, depends on your age, income and family circumstances. And of course, you have to live here full time and submit your annual declaration of income to the tax man.
All the details are on the government website but bear in mind that they might be 'revised' by Hollande and are unlikely to be revised upwards.
NB that applies mainly to taxe d'hab and to a lesser extent to foncière. I don't think other taxes such income tax and social charges are ever discounted...

+1
After the age of 75, my late English neighbour didn't pay Taxe d'Hab, since her income was so low. The age might have changed since her day.
"Unfortunately", OH's and my combined Pensions are above the limit and we pay Taxe d'Hab and Taxe F. in full.
A Mutuelle (Top-Up Insurance) is necessary as you get older, as the Social Security only reimburses about 70% of consultations, treatments, etc... (and peanuts for teeth and spectacles), unless you have an ALD (affection de longue-durée) where you have 100% coverage.
Our only perk as OAPs is the Carte Sénior with the SNCF and even then you have to pay for it (about 50€ each) annually.
As mentioned, any discounts available depend on your age, income and family circumstances.

Just for the avoidance of doubt or possible misunderstanding the 100% reimbursement for ALD is only for the specific ailment for which it is awarded and consequential related treatment.

I'm sure that's what DMU meant but it can be read differently

I concur having aliments that come under that category if you get treated for anything else it is business as normal.

You're both right, of course, it wasn't clear!
However many ALDs you might have, short-term ailments are reimbursed as usual, they are clearly separated on the "bizone" prescriptions. Therefore it's awlays advisable to take out a Mutuelle.
Sorry for the confusion....

On SNCF .you can still get cheaper fares without a card just use the 60+ box.

However as "the man in seat 61" says; the quota for the 60+ cheap fares may have been allocated , so always check to see if the standard fare is cheaper.

some Buses offer a discount as well.

Some pensioner and/or local discounts are given only to those paying the local taxes

I have to take medicines every day, but I still have to pay. I have been to the CPAM office so they know I have to take them for the rest of my life. I have to pay part to the pharmacy, and then I get a letter from CPAM asking for 50c a box, and since I need 2boxes a month, that's another €1. I know it's not much, but it's free in the UK, and I thought it would be free here, since I'm over 60 as well. At least I got my tax fonciere reduced - wait till you're 75 then it's free. I don't pay tax habitation, so I suppose it's swings and roundabouts. You have to pay council tax in UK no matter how little your pension. There is a scheme here which helps you pay for a mutuelle. It's not much, but it covers the basics. I've been told I could possibly get a sum of €500 pa towards a mutuelle through this scheme. Better than nothing!

This is just one of the differences between the UK and France. French pensioners are in the same boat and pay what's due unless they have a Mutuelle (or unless the ailment is an ALD).
Out of interest and for other members who haven't taken out a Mutuelle, can you give a link explaining the scheme for help to pay a Mutuelle? Is it offered by the Government?
As mentioned above, my elderly neighbour didn't have to pay the Taxe d'Habitation due to very low income, but still paid Taxe Foncière after the age of 75. I assumed that the Impôts consider that, since one is a property owner, one has the means to pay Property Tax. Can you give a link confirming no Taxe Foncière after the age of 75? It's too late for her, but this will interest a lot of over-70s on the forum!!

There is a simulator on the AMELI website that helps you find out whether you qualify for CMU-C or help with top-up (ACS)

ameli.fr - Simulateur d'aide financière

Probably the most dangerous assumption to make about anything.
It's a different country with a different government, a different culture, different ways of doing things, different retirement ages, different ways of getting your money off you, why would you expect things to work the same?
It's a bit like expecting the average French town to charge several euros for parking, because that's what the average UK town does - but you don't hear many expats in France wingeing about that.

Using my former neighbour again as an example, she was eligible for CMU, but what lot of paperwork to provide beforehand and what a wait, because the Commissions only meet up quarterly. And then exactly the same documents to provide every year thereafter. An annual head-ache for her neighbour (= me)...
According to the AMELI site, unless she has family dependants living with her, 500€ towards paying Miss L's Mutuelle (ACS) seems optimistic, but whatever sum she'd be entitled to, there will always be the same paperwork to remit.
Fore-warned is fore-armed!