Old thread, but it appears that no one correctly answered the OP, so in case any one else stumbles across this thread like I did, here goes:
In Transmit, open Preferences and in the General tab, toggle the pop-up menu to select Transmit as the "Default FTP client". This SHOULD cause Safari and other browsers to use use Transmit as the client.
Every ftp client app I've seen has this setting; no browsers, unfortunately, seem to have this setting. sFTP is usually a separate setting. The "Default App" app mentioned above will also work, but I generally avoid installing 3rd party software (especially something like a preference pane) unless there is no simpler solution or unless I expect to use it repeatedly.
If this fails to actually change the default ftp client, then you may need to refer to this thread:
https://discussions.apple.com/thread/2300543?start=0&tstart=0
which covers editing/rebuilding/replacing the launch services database.
PS: this thread is a striking example of responders seeing a key word such as "ftp client" or "Speed Download" and spewing out a canned answer without actually answering the question the OP was asking - amazing that people can get to Level 7 or Level 9 with such off-base answers as those posted above.
Message was edited by: BTB83