This paper examines the benefits and constraints of applying blockchain technology for the Paris Agreement carbon market mechanism and develops a list of technical requirements and soft factors as selection criteria to test the feasibility of two different blockchain platforms. The carbon market mechanism, as outlined in Article 6.2 of the Paris Agreement, can accelerate climate action by enabling cooperation between national Parties. However, in the past, carbon markets were limited by several constraints. Our research investigates these constraints and translates them into selection criteria to design a blockchain platform to overcome these past limitations. The developed selection criteria and assumptions developed in this paper provide an orientation for blockchain assessments. Using the selection criteria, we examine the feasibility of two distinct blockchains, Ethereum and Hyperledger Fabric, for the specific use case of Article 6.2. These two blockchain systems represent contrary forms of design and governance; Ethereum constitutes a public and permissionless blockchain governance system, while Hyperledger Fabric represents a private and permissioned governance system. Our results show that both blockchain systems can address present carbon market constraints by enhancing market transparency, increasing process automation, and preventing double counting. The final selection and blockchain system implementation will first be possible, when the Article 6 negotiations are concluded, and governance preferences of national Parties are established. Our paper informs about the viability of different blockchain systems, offers insights into governance options, and provides a valuable framework for a concrete blockchain selection in the future.