Question: My wife is an Thai national with an Thai passport. She holds an spouse/partner leave to remain in the UK residence permit. Does she need to apply for a Schengen visa before travelling to France or any other Schengen countries? And if so does she need to apply for a separate Schengen visas for each planned trip (eg France in May, Austria in July, Malta in September etc)

Answer: 
Yes, I think she will need Schengen visa. Since you are an EU citizen she has a *right* to get it, and per EU rules the visa will be granted for free and "as quickly as possible".

You can apply for multiple-entry Schengen visa, but it's up to the embassy whether to grant it or not. Some countries are more strict than others. Having approximate travel plans usually helps, especially if it's to the same country. E.g. if you demonstrate intent to travel to France multiple times over next year, French embassy is likely to issue multiple entry visa for a year. You can then use this visa to enter any schengen country.

Now, all of above applies to EU citizens. As you may know UK is stated to exit EU on March 29, which is before you planned trip in May. It's anyone's guess at this point what will happen on March 29 and what rules will be in place after it.
Yes, according to <https://ec.europa.eu/home-affairs/what-we-do/policies/borders-and-visas/visa-policy/apply_for_a_visa_en> Thai nationals require a visa to enter Schengen. The application rules generally require you to apply to the country relating to the main purpose of your trip / where you will spend the most time.