Front tooth is a partial denture, gap between teeth. How can I join them?

Without pictures it's impossible to answer your question. You may need additional veneers or bonding to make your smile more aesthetic and close the space. 

Not sure of which tooth you broke and want an implant? But I agree with you that widening one tooth to close both spaces would be too much width for that tooth. In smile design there is a principal of golden proportion. It states that everything in design has a certain proportion to other objects. Thus, it is the same with teeth. It sounds to me that at a minimum you may want to consider closing gaps by doing this with 4 front teeth at a minimum. If you do this then you can close the gaps and yet have normally proportioned teeth that will be a harmonious look of symmetry. As another possibility, you could consider orthodontics and move the teeth to close the gaps. You may need to do a combination of orthodontics and restorative with veneers or crowns. The point is you have options and that is great.