Is it ethical to apply for a short-term grant with a partner/spouse/girlfriend?
Provided you are qualified and intend to do a good job under the grant, I see no ethical considerations at all. Many people (most?) applying for grants in other countries have a variety of goals, not all of which are relevant to the position itself. Wanting to live in Paris is pretty common, I'd guess. 

There would be an issue if she is the decision maker on who gets the grant. In such a case she should recuse from the decision and pass it to others, such as a superior. But otherwise, there should be no problem.