I would like to provide my client with access to the roadmap section of Jira but I would like this to be read-only and I would like to ensure they are not able to access other areas over the Jira project such as the backlog and active sprint.
No, that is not possible. Although Jira has a pretty fine-grained permissions system, it is not related to specific features.
You can restrict access to a user to just viewing permissions, so people cannot create/edit issues or manipulate the order of items in the backlog, but they will be able to access the backlog or an active sprint.
For a more detailed overview of project permissions, see:
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