Modern noun [恋]{こい} ("love", generally referring more specifically to romantic or carnal love) is derived as the [連用形]{れんようけい} (also known as the "continuative form" or "stem form") of verb [恋う]{こう}.
The historical kana spelling for the verb ([歴史的仮名遣い]{れきしてきかなづかい}, see also the Wikipedia articles in Japanese and English) was [恋ふ]{こふ} instead, and the [連用形]{れんようけい} was [恋ひ]{こひ}.
→ With the [送り仮名]{おくりがな}, we know that [恋ひ]{こひ} is intended not as the noun, but rather as the [連用形]{れんようけい} of the verb. And [恋ふ]{こふ} must be understood as the verb.
⇒ As [恋ひ恋ふ]{こひこふ}, this could be parsed as a compound verb, and as a reduplication (where the same element shows up multiple times), it comes across as an intensifier: [吾が君]{わがきみ} doesn't just love, they really really love.
- Regarding the historical shift in kana spellings, Middle Japanese apparently pronounced the final ふ and ひ etc. closer to how they are spelled -- so the verb [恋ふ]{こふ} was pronounced as something like kofu. Over time, the medial (mid-word) //h// and //f// sounds lenited (softened) and vanished (almost) everywhere except before //a//, where we now have modern わ. This is why [買う]{かう} gets that //w// that appears in [買]{か}[わ]{●}ない.
For some more about this historical shift, read this post.