I received an offer from Germany. However, my husband is working in France. Both of us are immigrants with temporary residence permit. We don't have kids.
In this case, what is my tax class in Germany?
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You will be tax class 1.
When your spouse does not live in Germany and doesn't receive an income from Germany, then it is very unlikely that he needs to pay German income tax (he is not "unbeschränkt Einkommensteuerpflichtig" according to §1 EStG). When your spouse does not need to pay German income tax, then you are counted as if you were not married and get tax class 1 (§38b EStG).
But as Aganju mentioned in the comments, your tax class isn't actually that relevant. It is used to estimate very roughly how much tax you likely have to pay and is then used to calculate how much tax is deducted from your monthly salary. But how much you actually have to pay is decided when you do your taxes at the end of the year. The Finanzamt then checks how much tax was deducted over the year and pays (or bills) you the difference.
What does matter, however, is that you can not do tax splitting with your husband ("Ehegattensplitting") when he does not pay income tax in Germany. When you would be able to do that, you would have to pay less taxes, especially when your incomes are very different.