While paragliding, the shoes are not at all required when you are flying but are important when you are running for take-off and landing. This is because when you are taking off, you have to run for a few seconds with the pilot to gain uplift under the paraglider. And while landing, you have to run as well until you come to a complete stop - for a few seconds.
Most of the times, the landing is smooth and easy, but sometimes, it can be a bit rough or fast, this is when good quality shoes come in handy. So make sure you are wearing good sturdy shoes that, preferably, provide ankle support. Avoid wearing open footwear or anything that can come loose and fall off during the flight.