I've just checked and it seems that I can take out a Discovery + subscription for month and watch the TdF live. We usually enjoy watching the highlights on ITV4 but it would be good to have the option of live coverage. Hopefully I have got that right?
That's correct.
You need the £6.99/month "Standard" subscription for the cycling, and it auto-renews for the following month if you don't cancel before the end of your current period.
As well as the English and Multi-audio (choice of foreign language commentary, or none) no ads streams, you may also find streams that are Eurosport 1 or 2 as broadcast, complete with ads. Take note of any logos that show with the stream names.
There can be an interval (15-30 min?) between the live stream finishing, and the link for it appearing in the catchup/replay section.
I generally watch on my laptop via chrome, so I've no advice on TV apps.