Start with a single conversation with anyone you know who's remotely related to that industry (preferably someone in the industry, if you can). Look for second degree connections on LinkedIn to folks at companies in that industry and ask your mutual connection for an introduction. Treat these meetings as informational interviews where your goal is to soak up as much knowledge and info as possible - be curious, ask a lot of questions, and listen more than you speak. Always end the conversations by asking for other introductions to people they think might be relevant or helpful.
By the time you've finally understood the landscape, you've already started building your network in the space. You've likely been building your product during this time - probably by integrating with non-paywall publishers and smaller news outlets. Work your way into the smallest paywalled news source first and start having conversations about the value prop with them and why a partnership with you will be beneficial to them. From there work your way up to the bigger guys. Remember that it will take many conversations and you're building relationships - deals like this are not closed overnight.
Hope this helps - good luck!