Is it gram. correct to say Samantha's dog......

Yes. That's correct. You've used an apostrophe and s after Samantha to show that she possesses the dog.

Also for a country can I say France's policies...?

Yes. That's also correct. :-)

Thanks a lot.

You're very welcome.

Yes, it is grammatically correct to say "Samantha's dog" if you are referring to a dog that belongs to Samantha. The use of the possessive form "Samantha's" indicates ownership or association.

To determine if a sentence is grammatically correct, you can follow these steps:
1. Identify the subject (who or what the sentence is about) and the verb (what the subject is doing or being).
2. Identify any modifiers or additional words that clarify or describe the subject or verb.
3. Verify that the sentence follows the rules of grammar, such as subject-verb agreement, proper word order, and appropriate use of punctuation.

In this case, "Samantha's" is a possessive noun modifying the noun "dog." The sentence structure is correct, with the subject "Samantha's dog" followed by the verb (implicit or stated elsewhere in the sentence).