In such case you must model your entities this way:
public class Contract
{
   public virtual string ContractId { get; set; }
   public virtual ICollection<ContractPart> ContractParts { get; set; }
}
public class Part
{
   public virtual string PartId { get;set; }
   public virtual ICollection<ContractPart> ContractParts { get; set; }
}
public class ContractPart
{ 
   public virtual string  ContractId { get; set; }
   public virtual string PartId { get; set; }
   public virtual Contract Contract { get; set; }
   public virtual Part Part { get; set; }
   public virtual string Date { get; set; } //additional info
   public virtual decimal Price { get; set; } //additional info
}
In derived context you must define:
protected override void OnModelCreating(DbModelBuilder modelBuilder)
{
   modelBuilder.Entity<ContractPart>()
               .HasKey(cp => new { cp.ContractId, cp.PartId });
   modelBuilder.Entity<Contract>()
               .HasMany(c => c.ContractParts)
               .WithRequired()
               .HasForeignKey(cp => cp.ContractId);
   modelBuilder.Entity<Part>()
               .HasMany(p => p.ContractParts)
               .WithRequired()
               .HasForeignKey(cp => cp.PartId);  
}