In the first sentence, you should say "histories" (plural), because you are talking about two separate histories (the history of Britain and the history of France). You're saying they're similar to each other, but you're not saying that they're just one single history. Use "are," because you're talking about two things. In the second sentence, you're talking about just one thing: the weather forecast for a two-day period. Use "is," because the subject is singular. When you have multiple subjects that all possess something, it's correct to use the possessive marker ('s) only after the final term. For example, "John and Steven's cat is yellow." "John and Steven's cats are both yellow." You could say "France and Britain's histories are similar in some respects." Personally, for greater clarity, I would rewrite the sentence as "The histories of France and Britain are similar in some respects." The second sentence should be "Saturday and Sunday's forecast is..." Again, for greater clarity, you could also say "The forecast for Saturday and Sunday is..." or "The forecast for the weekend is..."

The first sentence use "Are"; and for the second use "is".

please