Begin a new Madden game (no loaded rosters, teams, franchises, etc.). At the menu screen, go to "Features", "Rosters", then "Trade Player". Find your desired team and trade the players you do not want for those that you do. All trades will be accepted, unlike in franchise mode. Save your roster under something easy to remember, load it, start a franchise, and start playing.
From the main menu, go to "Features", then "Rosters". Select "Release Player". Release any player that you want from any team. Then, go to franchise and select a team. Go to "Rosters", then "Free Agents". And all the players you released will be there, and you will be able to sign them to your team.
Getting all your favorite players on your team in franchise mode is a difficult task. Go through all the teams by selecting coaches for them; then trades are un-rejectable. Once your team's salary cap is too high, release and sign your players repeatedly until all them are as low as possible. Certain players must be signed to shorter than seven years to get them to drop. Some players will not accept a drop in salary at all, but if you release them again, you will find that they want less. You can keep doing this until they are low. However, there are a handful of players that you cannot do any of this with. This will clear up some room to get all the players you want. Also, you can do this to stack your other favorite teams. You can also create eight new custom teams in franchise mode. Do this, and you can kick your least favorite eight teams out of the league by replacing them. Wait until the end of the season to trade for the top draft picks; by then they are all set. Just select a coach, a team, and trade for the top seven picks then give the other top picks to your other created or favorite teams. To keep the teams you want good, and the ones that you dislike bad, select a coach and trade good players up at the end of each season. This entire process takes several days, but is great when completed.