Application for visa free transit (G)

I am a French national and my husband is English. We live in UK. We will be travelling from London UK to Beijing and will stay in the capital to visit family friends for less than 144 hours before heading to Seoul for a week before returning to our country of origin (UK, London). We have tickets booked and paid for to arrive in Beijing at 22:30 on 17 November before leaving at 16:50 for Seoul on 23 November. We are staying within Beijing area. Do we qualify for 144 hour free transit? Do we have to apply for confirmation of or get a document to confirm free status? Or do we simply arrive in Beijing and deal with it on arrival at the airport?If we need documents, what’s the cost? Who issues any confirmation or document?