As you said you have complete one week to travel into these two countries. I think this is not enough time, that's why you should only visit the main cities. Your start of the journey depends on the city you arrive first. I would assume you would arrive in Berlin or Frankfurt.
For the first day, you can travel in the city you arrive with the Tageskarte(Day ticket), which is valid throughout a day with all type of local transportations. For staying overnight you should plan before you arrive as during the Christmas time everything will be crowded because of holidays.
On the second day, you can leave for either Berlin or Frankfurt. There are many good places to visit there. For the Christmas night, I would recommend you to stay in Berlin. It's one of the best Christmas celebration places in the world.
After celebrating Christmas you can travel to France via train. There will be direct trains from both of these cities. You can directly go to Paris on the train. Paris is a great place for visitors. In this city, you can also travel with the day ticket. If your flight back to your place is from Germany, then you need to again come back to Germany in well advanced.
However, I would strongly recommend you to book your accommodation in well advanced, because of the holiday season. As you said you are traveling with a kid, it won't be that much difficult. For all the traveling tickets I think you can carry your kid without buying his tickets. Although, check the official rules before traveling.
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