To Touch
To Come Into Contact With, To Touch On
intransitive verb, transitive verb, ichidan verb
触る means "to touch," and 触れる also means to touch. The word also means to touch on, as in touching on some subject. Just think of a subject that is rare (れる) for you to want to touch on.
触れる is often for when something happens to come into contact with something, possibly in a fleeting or momentary way. It's still used in phrases like "When I touched your hand," but has a lighter, more indirect and literary feel than 触る, which conveys a greater sense of purpose and intent behind the action.
触れる is often used in constructions like 手がカバンに触れる (one's hand touches a bag), where が indicates what's doing the touching and に marks what's being touched. If you see を instead of が, 触れる becomes transitive, changing the meaning to "to have your hand touch a bag."
The reading is totally different from 触る so don't let that fool you. In this case, you feel some fur (ふれ).
この車にはお手を触れないようお願い申し上げます。
Kindly do not touch this car.
その話にはもう触れないでください。
Please don't touch on that topic again.
誰かが肩に触れるのを感じて振り返ったが、そこには誰もいなかった。
I felt somebody touch my shoulder and I looked back, but nobody was there.