The sentence should be changed as there is no subject-verb agreement. The correct form of the verb should be in plural instead of singular. So the correct sentence is “Both the ranger and the camper see the bear.”
Even though both subject nouns are singular (ranger and camper), the rule of compound subject applies here. In this case singular nouns are united by the preposition “and” to make a plural subject. Therefore, the verb should be in the plural (see) to have subject-verb agreement.