Question

claimed florida, texas, california; built missions
elected to texas congress; served as a voice for tejanos and supported annexation josé antonio navarro
elected second president of texas; moved texas capital to austin and forced many natives out of texas mirabeau b. lamar
claimed land in new world to profit from fur trading
franco spain

Explanation:

For the first row "Claimed Florida, Texas, California; built missions", Spain was known for claiming these areas and building missions in the Americas. For the fourth row "Claimed land in New World to profit from fur trading", France was involved in fur trading in the New World (like in areas such as Canada).

Answer:

First empty box: Spain
Fourth empty box: France