You can move the data from one system to the other, but the relationships, screens, etc would need to be redesigned and re-created in FileMaker. I believe Fox Pro stores the data as DBF files. FileMaker can import directly from DBF files--so that may be one way to move the data, but certain dbf files--such as memo fields don't import with complete success so you may have better luck exporting to a text file such as a tab or csv file and then importing into FileMaker.
You will probably find FMP very alien in some ways to the way you are used to.
FM doesnt do queries in the traditional sense.
For many things in FM you establish the relational structure of your database in a fairly static state. You can create as many of these "Joins" as you like as Relationships. These become very useful in designing forms and working with the data.
FM's unique approach to relational databases also gives you some extremely powerful and flexible tools. In some ways this is its shortfall too. Rather than forcing you into good/traditional relational database design the tool allows you to be more open ended to achieve what you want to accomplish. Once you begin to understand the differences you will find powerful ways to do things quickly that your other solutions would have required extensive coding or simply not been possible.
If you spend some time mapping the relational structure of your existing solution it will go a long way to helping you establish a good base for making the switch. Some things you do in one solution are completely different and often not needed in FM due to the overall approach the FM takes.
Queries and Finds are not simply synonymous.