Program - It means to set, modify, to regulate, produce a result, etc. Program can be both noun and verb As per US English – it can be used for anything.
As per UK English – program can be used only for things related to computers. Examples:
1. She asked the Tech geek to program the computer today.
2. Can you please program the alarm for 6 pm?
Programme - It means a plan of action for a specific purpose; list of acts or activities related to an event. This can only be a noun; Not prevalent in US English but as per British English, programme is used to refer to TV shows, Agenda of meeting or any event, collection of projects etc. Examples:
1. He was disheartened to know that his name was not there for the programme.
2. My mother watches this TV programme on repeat mode.